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<h1 class="title">QMatrix4x4 Class Reference</h1>
<!-- $$$QMatrix4x4-brief -->
<p>The QMatrix4x4 class represents a 4x4 transformation matrix in 3D space. <a href="#details">More...</a></p>
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<pre class="cpp"> <span class="preprocessor">#include <QMatrix4x4></span></pre><p>This class was introduced in Qt 4.6.</p>
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<h2>Public Functions</h2>
<table class="alignedsummary">
<tr><td class="memItemLeft rightAlign topAlign"> </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#QMatrix4x4">QMatrix4x4</a></b> ()</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#QMatrix4x4-2">QMatrix4x4</a></b> ( const qreal * <i>values</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#QMatrix4x4-3">QMatrix4x4</a></b> ( qreal <i>m11</i>, qreal <i>m12</i>, qreal <i>m13</i>, qreal <i>m14</i>, qreal <i>m21</i>, qreal <i>m22</i>, qreal <i>m23</i>, qreal <i>m24</i>, qreal <i>m31</i>, qreal <i>m32</i>, qreal <i>m33</i>, qreal <i>m34</i>, qreal <i>m41</i>, qreal <i>m42</i>, qreal <i>m43</i>, qreal <i>m44</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#QMatrix4x4-4">QMatrix4x4</a></b> ( const QGenericMatrix<N, M, qreal> & <i>matrix</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#QMatrix4x4-6">QMatrix4x4</a></b> ( const QTransform & <i>transform</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#QMatrix4x4-7">QMatrix4x4</a></b> ( const QMatrix & <i>matrix</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QVector4D </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#column">column</a></b> ( int <i>index</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> const qreal * </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#constData">constData</a></b> () const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#copyDataTo">copyDataTo</a></b> ( qreal * <i>values</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> qreal * </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#data">data</a></b> ()</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> const qreal * </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#data-2">data</a></b> () const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> qreal </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#determinant">determinant</a></b> () const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#fill">fill</a></b> ( qreal <i>value</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#flipCoordinates">flipCoordinates</a></b> ()</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#frustum">frustum</a></b> ( qreal <i>left</i>, qreal <i>right</i>, qreal <i>bottom</i>, qreal <i>top</i>, qreal <i>nearPlane</i>, qreal <i>farPlane</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#inverted">inverted</a></b> ( bool * <i>invertible</i> = 0 ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> bool </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#isIdentity">isIdentity</a></b> () const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#lookAt">lookAt</a></b> ( const QVector3D & <i>eye</i>, const QVector3D & <i>center</i>, const QVector3D & <i>up</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QPoint </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#map">map</a></b> ( const QPoint & <i>point</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QPointF </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#map-2">map</a></b> ( const QPointF & <i>point</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QVector3D </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#map-3">map</a></b> ( const QVector3D & <i>point</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QVector4D </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#map-4">map</a></b> ( const QVector4D & <i>point</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QRect </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#mapRect">mapRect</a></b> ( const QRect & <i>rect</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QRectF </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#mapRect-2">mapRect</a></b> ( const QRectF & <i>rect</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QVector3D </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#mapVector">mapVector</a></b> ( const QVector3D & <i>vector</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix3x3 </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#normalMatrix">normalMatrix</a></b> () const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#optimize">optimize</a></b> ()</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#ortho">ortho</a></b> ( qreal <i>left</i>, qreal <i>right</i>, qreal <i>bottom</i>, qreal <i>top</i>, qreal <i>nearPlane</i>, qreal <i>farPlane</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#ortho-2">ortho</a></b> ( const QRect & <i>rect</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#ortho-3">ortho</a></b> ( const QRectF & <i>rect</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#perspective">perspective</a></b> ( qreal <i>angle</i>, qreal <i>aspect</i>, qreal <i>nearPlane</i>, qreal <i>farPlane</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#rotate">rotate</a></b> ( qreal <i>angle</i>, const QVector3D & <i>vector</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#rotate-2">rotate</a></b> ( const QQuaternion & <i>quaternion</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#rotate-3">rotate</a></b> ( qreal <i>angle</i>, qreal <i>x</i>, qreal <i>y</i>, qreal <i>z</i> = 0.0f )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QVector4D </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#row">row</a></b> ( int <i>index</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#scale">scale</a></b> ( const QVector3D & <i>vector</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#scale-2">scale</a></b> ( qreal <i>x</i>, qreal <i>y</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#scale-3">scale</a></b> ( qreal <i>x</i>, qreal <i>y</i>, qreal <i>z</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#scale-4">scale</a></b> ( qreal <i>factor</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#setColumn">setColumn</a></b> ( int <i>index</i>, const QVector4D & <i>value</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#setRow">setRow</a></b> ( int <i>index</i>, const QVector4D & <i>value</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#setToIdentity">setToIdentity</a></b> ()</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#toAffine">toAffine</a></b> () const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QGenericMatrix<N, M, qreal> </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#toGenericMatrix">toGenericMatrix</a></b> () const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QTransform </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#toTransform">toTransform</a></b> () const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QTransform </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#toTransform-2">toTransform</a></b> ( qreal <i>distanceToPlane</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#translate">translate</a></b> ( const QVector3D & <i>vector</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#translate-2">translate</a></b> ( qreal <i>x</i>, qreal <i>y</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> void </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#translate-3">translate</a></b> ( qreal <i>x</i>, qreal <i>y</i>, qreal <i>z</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#transposed">transposed</a></b> () const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-QVariant">operator QVariant</a></b> () const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> bool </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-not-eq">operator!=</a></b> ( const QMatrix4x4 & <i>other</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> const qreal & </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-28-29">operator()</a></b> ( int <i>row</i>, int <i>column</i> ) const</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> qreal & </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-28-29-2">operator()</a></b> ( int <i>row</i>, int <i>column</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 & </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-eq">operator*=</a></b> ( const QMatrix4x4 & <i>other</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 & </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-eq-2">operator*=</a></b> ( qreal <i>factor</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 & </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2b-eq">operator+=</a></b> ( const QMatrix4x4 & <i>other</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 & </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator--eq">operator-=</a></b> ( const QMatrix4x4 & <i>other</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 & </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2f-eq">operator/=</a></b> ( qreal <i>divisor</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> bool </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-eq-eq">operator==</a></b> ( const QMatrix4x4 & <i>other</i> ) const</td></tr>
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<h2>Related Non-Members</h2>
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<tr><td class="memItemLeft rightAlign topAlign"> bool </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#qFuzzyCompare-2">qFuzzyCompare</a></b> ( const QMatrix4x4 & <i>m1</i>, const QMatrix4x4 & <i>m2</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-4">operator*</a></b> ( const QMatrix4x4 & <i>m1</i>, const QMatrix4x4 & <i>m2</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QVector3D </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-5">operator*</a></b> ( const QVector3D & <i>vector</i>, const QMatrix4x4 & <i>matrix</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QVector3D </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-6">operator*</a></b> ( const QMatrix4x4 & <i>matrix</i>, const QVector3D & <i>vector</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QVector4D </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-7">operator*</a></b> ( const QVector4D & <i>vector</i>, const QMatrix4x4 & <i>matrix</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QVector4D </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-8">operator*</a></b> ( const QMatrix4x4 & <i>matrix</i>, const QVector4D & <i>vector</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QPoint </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-9">operator*</a></b> ( const QPoint & <i>point</i>, const QMatrix4x4 & <i>matrix</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QPointF </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-10">operator*</a></b> ( const QPointF & <i>point</i>, const QMatrix4x4 & <i>matrix</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QPoint </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-11">operator*</a></b> ( const QMatrix4x4 & <i>matrix</i>, const QPoint & <i>point</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QPointF </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-12">operator*</a></b> ( const QMatrix4x4 & <i>matrix</i>, const QPointF & <i>point</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-13">operator*</a></b> ( qreal <i>factor</i>, const QMatrix4x4 & <i>matrix</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2a-14">operator*</a></b> ( const QMatrix4x4 & <i>matrix</i>, qreal <i>factor</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2b-2">operator+</a></b> ( const QMatrix4x4 & <i>m1</i>, const QMatrix4x4 & <i>m2</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator--2">operator-</a></b> ( const QMatrix4x4 & <i>m1</i>, const QMatrix4x4 & <i>m2</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator--24">operator-</a></b> ( const QMatrix4x4 & <i>matrix</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QMatrix4x4 </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-2f-2">operator/</a></b> ( const QMatrix4x4 & <i>matrix</i>, qreal <i>divisor</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QDataStream & </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-lt-lt-25">operator<<</a></b> ( QDataStream & <i>stream</i>, const QMatrix4x4 & <i>matrix</i> )</td></tr>
<tr><td class="memItemLeft rightAlign topAlign"> QDataStream & </td><td class="memItemRight bottomAlign"><b><a href="qmatrix4x4.html#operator-gt-gt-15">operator>></a></b> ( QDataStream & <i>stream</i>, QMatrix4x4 & <i>matrix</i> )</td></tr>
</table>
<a name="details"></a>
<!-- $$$QMatrix4x4-description -->
<div class="descr">
<h2>Detailed Description</h2>
<p>The QMatrix4x4 class represents a 4x4 transformation matrix in 3D space.</p>
</div>
<p><b>See also </b><a href="qvector3d.html">QVector3D</a> and <a href="qgenericmatrix.html">QGenericMatrix</a>.</p>
<!-- @@@QMatrix4x4 -->
<div class="func">
<h2>Member Function Documentation</h2>
<!-- $$$QMatrix4x4[overload1]$$$QMatrix4x4 -->
<h3 class="fn"><a name="QMatrix4x4"></a>QMatrix4x4::<span class="name">QMatrix4x4</span> ()</h3>
<p>Constructs an identity matrix.</p>
<!-- @@@QMatrix4x4 -->
<!-- $$$QMatrix4x4$$$QMatrix4x4constqreal* -->
<h3 class="fn"><a name="QMatrix4x4-2"></a>QMatrix4x4::<span class="name">QMatrix4x4</span> ( const <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> * <i>values</i> )</h3>
<p>Constructs a matrix from the given 16 floating-point <i>values</i>. The contents of the array <i>values</i> is assumed to be in row-major order.</p>
<p>If the matrix has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to <a href="qmatrix4x4.html#optimize">optimize</a>() if they wish <a href="qmatrix4x4.html">QMatrix4x4</a> to optimize further calls to <a href="qmatrix4x4.html#translate">translate</a>(), <a href="qmatrix4x4.html#scale">scale</a>(), etc.</p>
<p><b>See also </b><a href="qmatrix4x4.html#copyDataTo">copyDataTo</a>() and <a href="qmatrix4x4.html#optimize">optimize</a>().</p>
<!-- @@@QMatrix4x4 -->
<!-- $$$QMatrix4x4$$$QMatrix4x4qrealqrealqrealqrealqrealqrealqrealqrealqrealqrealqrealqrealqrealqrealqrealqreal -->
<h3 class="fn"><a name="QMatrix4x4-3"></a>QMatrix4x4::<span class="name">QMatrix4x4</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m11</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m12</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m13</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m14</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m21</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m22</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m23</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m24</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m31</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m32</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m33</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m34</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m41</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m42</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m43</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>m44</i> )</h3>
<p>Constructs a matrix from the 16 elements <i>m11</i>, <i>m12</i>, <i>m13</i>, <i>m14</i>, <i>m21</i>, <i>m22</i>, <i>m23</i>, <i>m24</i>, <i>m31</i>, <i>m32</i>, <i>m33</i>, <i>m34</i>, <i>m41</i>, <i>m42</i>, <i>m43</i>, and <i>m44</i>. The elements are specified in row-major order.</p>
<p>If the matrix has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to <a href="qmatrix4x4.html#optimize">optimize</a>() if they wish <a href="qmatrix4x4.html">QMatrix4x4</a> to optimize further calls to <a href="qmatrix4x4.html#translate">translate</a>(), <a href="qmatrix4x4.html#scale">scale</a>(), etc.</p>
<p><b>See also </b><a href="qmatrix4x4.html#optimize">optimize</a>().</p>
<!-- @@@QMatrix4x4 -->
<!-- $$$QMatrix4x4$$$QMatrix4x4constQGenericMatrix<N,M,qreal>& -->
<h3 class="fn"><a name="QMatrix4x4-4"></a>QMatrix4x4::<span class="name">QMatrix4x4</span> ( const <span class="type"><a href="qgenericmatrix.html">QGenericMatrix</a></span><<span class="type">N</span>, <span class="type">M</span>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span>> & <i>matrix</i> )</h3>
<p>Constructs a 4x4 matrix from the left-most 4 columns and top-most 4 rows of <i>matrix</i>. If <i>matrix</i> has less than 4 columns or rows, the remaining elements are filled with elements from the identity matrix.</p>
<p><b>See also </b><a href="qmatrix4x4.html#toGenericMatrix">toGenericMatrix</a>().</p>
<!-- @@@QMatrix4x4 -->
<!-- $$$QMatrix4x4$$$QMatrix4x4constQTransform& -->
<h3 class="fn"><a name="QMatrix4x4-6"></a>QMatrix4x4::<span class="name">QMatrix4x4</span> ( const <span class="type"><a href="qtransform.html">QTransform</a></span> & <i>transform</i> )</h3>
<p>Constructs a 4x4 matrix from the conventional Qt 2D transformation matrix <i>transform</i>.</p>
<p>If <i>transform</i> has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to <a href="qmatrix4x4.html#optimize">optimize</a>() if they wish <a href="qmatrix4x4.html">QMatrix4x4</a> to optimize further calls to <a href="qmatrix4x4.html#translate">translate</a>(), <a href="qmatrix4x4.html#scale">scale</a>(), etc.</p>
<p><b>See also </b><a href="qmatrix4x4.html#toTransform">toTransform</a>() and <a href="qmatrix4x4.html#optimize">optimize</a>().</p>
<!-- @@@QMatrix4x4 -->
<!-- $$$QMatrix4x4$$$QMatrix4x4constQMatrix& -->
<h3 class="fn"><a name="QMatrix4x4-7"></a>QMatrix4x4::<span class="name">QMatrix4x4</span> ( const <span class="type"><a href="qmatrix.html">QMatrix</a></span> & <i>matrix</i> )</h3>
<p>Constructs a 4x4 matrix from a conventional Qt 2D affine transformation <i>matrix</i>.</p>
<p>If <i>matrix</i> has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to <a href="qmatrix4x4.html#optimize">optimize</a>() if they wish <a href="qmatrix4x4.html">QMatrix4x4</a> to optimize further calls to <a href="qmatrix4x4.html#translate">translate</a>(), <a href="qmatrix4x4.html#scale">scale</a>(), etc.</p>
<p><b>See also </b><a href="qmatrix4x4.html#toAffine">toAffine</a>() and <a href="qmatrix4x4.html#optimize">optimize</a>().</p>
<!-- @@@QMatrix4x4 -->
<!-- $$$column[overload1]$$$columnint -->
<h3 class="fn"><a name="column"></a><span class="type"><a href="qvector4d.html">QVector4D</a></span> QMatrix4x4::<span class="name">column</span> ( <span class="type">int</span> <i>index</i> ) const</h3>
<p>Returns the elements of column <i>index</i> as a 4D vector.</p>
<p><b>See also </b><a href="qmatrix4x4.html#setColumn">setColumn</a>() and <a href="qmatrix4x4.html#row">row</a>().</p>
<!-- @@@column -->
<!-- $$$constData[overload1]$$$constData -->
<h3 class="fn"><a name="constData"></a>const <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> * QMatrix4x4::<span class="name">constData</span> () const</h3>
<p>Returns a constant pointer to the raw data of this matrix.</p>
<p><b>See also </b><a href="qmatrix4x4.html#data">data</a>().</p>
<!-- @@@constData -->
<!-- $$$copyDataTo[overload1]$$$copyDataToqreal* -->
<h3 class="fn"><a name="copyDataTo"></a><span class="type">void</span> QMatrix4x4::<span class="name">copyDataTo</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> * <i>values</i> ) const</h3>
<p>Retrieves the 16 items in this matrix and copies them to <i>values</i> in row-major order.</p>
<!-- @@@copyDataTo -->
<!-- $$$data[overload1]$$$data -->
<h3 class="fn"><a name="data"></a><span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> * QMatrix4x4::<span class="name">data</span> ()</h3>
<p>Returns a pointer to the raw data of this matrix.</p>
<p><b>See also </b><a href="qmatrix4x4.html#constData">constData</a>() and <a href="qmatrix4x4.html#optimize">optimize</a>().</p>
<!-- @@@data -->
<!-- $$$data$$$data -->
<h3 class="fn"><a name="data-2"></a>const <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> * QMatrix4x4::<span class="name">data</span> () const</h3>
<p>Returns a constant pointer to the raw data of this matrix.</p>
<p><b>See also </b><a href="qmatrix4x4.html#constData">constData</a>().</p>
<!-- @@@data -->
<!-- $$$determinant[overload1]$$$determinant -->
<h3 class="fn"><a name="determinant"></a><span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> QMatrix4x4::<span class="name">determinant</span> () const</h3>
<p>Returns the determinant of this matrix.</p>
<!-- @@@determinant -->
<!-- $$$fill[overload1]$$$fillqreal -->
<h3 class="fn"><a name="fill"></a><span class="type">void</span> QMatrix4x4::<span class="name">fill</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>value</i> )</h3>
<p>Fills all elements of this matrx with <i>value</i>.</p>
<!-- @@@fill -->
<!-- $$$flipCoordinates[overload1]$$$flipCoordinates -->
<h3 class="fn"><a name="flipCoordinates"></a><span class="type">void</span> QMatrix4x4::<span class="name">flipCoordinates</span> ()</h3>
<p>Flips between right-handed and left-handed coordinate systems by multiplying the y and z co-ordinates by -1. This is normally used to create a left-handed orthographic view without scaling the viewport as <a href="qmatrix4x4.html#ortho">ortho</a>() does.</p>
<p><b>See also </b><a href="qmatrix4x4.html#ortho">ortho</a>().</p>
<!-- @@@flipCoordinates -->
<!-- $$$frustum[overload1]$$$frustumqrealqrealqrealqrealqrealqreal -->
<h3 class="fn"><a name="frustum"></a><span class="type">void</span> QMatrix4x4::<span class="name">frustum</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>left</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>right</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>bottom</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>top</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>nearPlane</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>farPlane</i> )</h3>
<p>Multiplies this matrix by another that applies a perspective frustum projection for a window with lower-left corner (<i>left</i>, <i>bottom</i>), upper-right corner (<i>right</i>, <i>top</i>), and the specified <i>nearPlane</i> and <i>farPlane</i> clipping planes.</p>
<p><b>See also </b><a href="qmatrix4x4.html#ortho">ortho</a>() and <a href="qmatrix4x4.html#perspective">perspective</a>().</p>
<!-- @@@frustum -->
<!-- $$$inverted[overload1]$$$invertedbool* -->
<h3 class="fn"><a name="inverted"></a><span class="type">QMatrix4x4</span> QMatrix4x4::<span class="name">inverted</span> ( <span class="type">bool</span> * <i>invertible</i> = 0 ) const</h3>
<p>Returns the inverse of this matrix. Returns the identity if this matrix cannot be inverted; i.e. <a href="qmatrix4x4.html#determinant">determinant</a>() is zero. If <i>invertible</i> is not null, then true will be written to that location if the matrix can be inverted; false otherwise.</p>
<p>If the matrix is recognized as the identity or an orthonormal matrix, then this function will quickly invert the matrix using optimized routines.</p>
<p><b>See also </b><a href="qmatrix4x4.html#determinant">determinant</a>() and <a href="qmatrix4x4.html#normalMatrix">normalMatrix</a>().</p>
<!-- @@@inverted -->
<!-- $$$isIdentity[overload1]$$$isIdentity -->
<h3 class="fn"><a name="isIdentity"></a><span class="type">bool</span> QMatrix4x4::<span class="name">isIdentity</span> () const</h3>
<p>Returns true if this matrix is the identity; false otherwise.</p>
<p><b>See also </b><a href="qmatrix4x4.html#setToIdentity">setToIdentity</a>().</p>
<!-- @@@isIdentity -->
<!-- $$$lookAt[overload1]$$$lookAtconstQVector3D&constQVector3D&constQVector3D& -->
<h3 class="fn"><a name="lookAt"></a><span class="type">void</span> QMatrix4x4::<span class="name">lookAt</span> ( const <span class="type"><a href="qvector3d.html">QVector3D</a></span> & <i>eye</i>, const <span class="type"><a href="qvector3d.html">QVector3D</a></span> & <i>center</i>, const <span class="type"><a href="qvector3d.html">QVector3D</a></span> & <i>up</i> )</h3>
<p>Multiplies this matrix by another that applies an <i>eye</i> position transformation. The <i>center</i> value indicates the center of the view that the <i>eye</i> is looking at. The <i>up</i> value indicates which direction should be considered up with respect to the <i>eye</i>.</p>
<!-- @@@lookAt -->
<!-- $$$map[overload1]$$$mapconstQPoint& -->
<h3 class="fn"><a name="map"></a><span class="type"><a href="qpoint.html">QPoint</a></span> QMatrix4x4::<span class="name">map</span> ( const <span class="type"><a href="qpoint.html">QPoint</a></span> & <i>point</i> ) const</h3>
<p>Maps <i>point</i> by multiplying this matrix by <i>point</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#mapRect">mapRect</a>().</p>
<!-- @@@map -->
<!-- $$$map$$$mapconstQPointF& -->
<h3 class="fn"><a name="map-2"></a><span class="type"><a href="qpointf.html">QPointF</a></span> QMatrix4x4::<span class="name">map</span> ( const <span class="type"><a href="qpointf.html">QPointF</a></span> & <i>point</i> ) const</h3>
<p>Maps <i>point</i> by multiplying this matrix by <i>point</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#mapRect">mapRect</a>().</p>
<!-- @@@map -->
<!-- $$$map$$$mapconstQVector3D& -->
<h3 class="fn"><a name="map-3"></a><span class="type"><a href="qvector3d.html">QVector3D</a></span> QMatrix4x4::<span class="name">map</span> ( const <span class="type"><a href="qvector3d.html">QVector3D</a></span> & <i>point</i> ) const</h3>
<p>Maps <i>point</i> by multiplying this matrix by <i>point</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#mapRect">mapRect</a>() and <a href="qmatrix4x4.html#mapVector">mapVector</a>().</p>
<!-- @@@map -->
<!-- $$$map$$$mapconstQVector4D& -->
<h3 class="fn"><a name="map-4"></a><span class="type"><a href="qvector4d.html">QVector4D</a></span> QMatrix4x4::<span class="name">map</span> ( const <span class="type"><a href="qvector4d.html">QVector4D</a></span> & <i>point</i> ) const</h3>
<p>Maps <i>point</i> by multiplying this matrix by <i>point</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#mapRect">mapRect</a>().</p>
<!-- @@@map -->
<!-- $$$mapRect[overload1]$$$mapRectconstQRect& -->
<h3 class="fn"><a name="mapRect"></a><span class="type"><a href="qrect.html">QRect</a></span> QMatrix4x4::<span class="name">mapRect</span> ( const <span class="type"><a href="qrect.html">QRect</a></span> & <i>rect</i> ) const</h3>
<p>Maps <i>rect</i> by multiplying this matrix by the corners of <i>rect</i> 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.</p>
<p><b>See also </b><a href="qmatrix4x4.html#map">map</a>().</p>
<!-- @@@mapRect -->
<!-- $$$mapRect$$$mapRectconstQRectF& -->
<h3 class="fn"><a name="mapRect-2"></a><span class="type"><a href="qrectf.html">QRectF</a></span> QMatrix4x4::<span class="name">mapRect</span> ( const <span class="type"><a href="qrectf.html">QRectF</a></span> & <i>rect</i> ) const</h3>
<p>Maps <i>rect</i> by multiplying this matrix by the corners of <i>rect</i> 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.</p>
<p><b>See also </b><a href="qmatrix4x4.html#map">map</a>().</p>
<!-- @@@mapRect -->
<!-- $$$mapVector[overload1]$$$mapVectorconstQVector3D& -->
<h3 class="fn"><a name="mapVector"></a><span class="type"><a href="qvector3d.html">QVector3D</a></span> QMatrix4x4::<span class="name">mapVector</span> ( const <span class="type"><a href="qvector3d.html">QVector3D</a></span> & <i>vector</i> ) const</h3>
<p>Maps <i>vector</i> by multiplying the top 3x3 portion of this matrix by <i>vector</i>. The translation and projection components of this matrix are ignored.</p>
<p><b>See also </b><a href="qmatrix4x4.html#map">map</a>().</p>
<!-- @@@mapVector -->
<!-- $$$normalMatrix[overload1]$$$normalMatrix -->
<h3 class="fn"><a name="normalMatrix"></a><span class="type"><a href="qgenericmatrix.html#QMatrix3x3-typedef">QMatrix3x3</a></span> QMatrix4x4::<span class="name">normalMatrix</span> () const</h3>
<p>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.</p>
<p><b>See also </b><a href="qmatrix4x4.html#inverted">inverted</a>().</p>
<!-- @@@normalMatrix -->
<!-- $$$optimize[overload1]$$$optimize -->
<h3 class="fn"><a name="optimize"></a><span class="type">void</span> QMatrix4x4::<span class="name">optimize</span> ()</h3>
<p>Optimize the usage of this matrix from its current elements.</p>
<p>Some operations such as <a href="qmatrix4x4.html#translate">translate</a>(), <a href="qmatrix4x4.html#scale">scale</a>(), and <a href="qmatrix4x4.html#rotate">rotate</a>() can be performed more efficiently if the matrix being modified is already known to be the identity, a previous <a href="qmatrix4x4.html#translate">translate</a>(), a previous <a href="qmatrix4x4.html#scale">scale</a>(), etc.</p>
<p>Normally the <a href="qmatrix4x4.html">QMatrix4x4</a> class keeps track of this special type internally as operations are performed. However, if the matrix is modified directly with operator()() or <a href="qmatrix4x4.html#data">data</a>(), then <a href="qmatrix4x4.html">QMatrix4x4</a> will lose track of the special type and will revert to the safest but least efficient operations thereafter.</p>
<p>By calling optimize() after directly modifying the matrix, the programmer can force <a href="qmatrix4x4.html">QMatrix4x4</a> to recover the special type if the elements appear to conform to one of the known optimized types.</p>
<p><b>See also </b><a href="qmatrix4x4.html#operator-28-29">operator</a>()(), <a href="qmatrix4x4.html#data">data</a>(), and <a href="qmatrix4x4.html#translate">translate</a>().</p>
<!-- @@@optimize -->
<!-- $$$ortho[overload1]$$$orthoqrealqrealqrealqrealqrealqreal -->
<h3 class="fn"><a name="ortho"></a><span class="type">void</span> QMatrix4x4::<span class="name">ortho</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>left</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>right</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>bottom</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>top</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>nearPlane</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>farPlane</i> )</h3>
<p>Multiplies this matrix by another that applies an orthographic projection for a window with lower-left corner (<i>left</i>, <i>bottom</i>), upper-right corner (<i>right</i>, <i>top</i>), and the specified <i>nearPlane</i> and <i>farPlane</i> clipping planes.</p>
<p><b>See also </b><a href="qmatrix4x4.html#frustum">frustum</a>() and <a href="qmatrix4x4.html#perspective">perspective</a>().</p>
<!-- @@@ortho -->
<!-- $$$ortho$$$orthoconstQRect& -->
<h3 class="fn"><a name="ortho-2"></a><span class="type">void</span> QMatrix4x4::<span class="name">ortho</span> ( const <span class="type"><a href="qrect.html">QRect</a></span> & <i>rect</i> )</h3>
<p>This is an overloaded function.</p>
<p>Multiplies this matrix by another that applies an orthographic projection for a window with boundaries specified by <i>rect</i>. The near and far clipping planes will be -1 and 1 respectively.</p>
<p><b>See also </b><a href="qmatrix4x4.html#frustum">frustum</a>() and <a href="qmatrix4x4.html#perspective">perspective</a>().</p>
<!-- @@@ortho -->
<!-- $$$ortho$$$orthoconstQRectF& -->
<h3 class="fn"><a name="ortho-3"></a><span class="type">void</span> QMatrix4x4::<span class="name">ortho</span> ( const <span class="type"><a href="qrectf.html">QRectF</a></span> & <i>rect</i> )</h3>
<p>This is an overloaded function.</p>
<p>Multiplies this matrix by another that applies an orthographic projection for a window with boundaries specified by <i>rect</i>. The near and far clipping planes will be -1 and 1 respectively.</p>
<p><b>See also </b><a href="qmatrix4x4.html#frustum">frustum</a>() and <a href="qmatrix4x4.html#perspective">perspective</a>().</p>
<!-- @@@ortho -->
<!-- $$$perspective[overload1]$$$perspectiveqrealqrealqrealqreal -->
<h3 class="fn"><a name="perspective"></a><span class="type">void</span> QMatrix4x4::<span class="name">perspective</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>angle</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>aspect</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>nearPlane</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>farPlane</i> )</h3>
<p>Multiplies this matrix by another that applies a perspective projection. The field of view will be <i>angle</i> degrees within a window with a given <i>aspect</i> ratio. The projection will have the specified <i>nearPlane</i> and <i>farPlane</i> clipping planes.</p>
<p><b>See also </b><a href="qmatrix4x4.html#ortho">ortho</a>() and <a href="qmatrix4x4.html#frustum">frustum</a>().</p>
<!-- @@@perspective -->
<!-- $$$rotate[overload1]$$$rotateqrealconstQVector3D& -->
<h3 class="fn"><a name="rotate"></a><span class="type">void</span> QMatrix4x4::<span class="name">rotate</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>angle</i>, const <span class="type"><a href="qvector3d.html">QVector3D</a></span> & <i>vector</i> )</h3>
<p>Multiples this matrix by another that rotates coordinates through <i>angle</i> degrees about <i>vector</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#scale">scale</a>() and <a href="qmatrix4x4.html#translate">translate</a>().</p>
<!-- @@@rotate -->
<!-- $$$rotate$$$rotateconstQQuaternion& -->
<h3 class="fn"><a name="rotate-2"></a><span class="type">void</span> QMatrix4x4::<span class="name">rotate</span> ( const <span class="type"><a href="qquaternion.html">QQuaternion</a></span> & <i>quaternion</i> )</h3>
<p>Multiples this matrix by another that rotates coordinates according to a specified <i>quaternion</i>. The <i>quaternion</i> is assumed to have been normalized.</p>
<p><b>See also </b><a href="qmatrix4x4.html#scale">scale</a>(), <a href="qmatrix4x4.html#translate">translate</a>(), and <a href="qquaternion.html">QQuaternion</a>.</p>
<!-- @@@rotate -->
<!-- $$$rotate$$$rotateqrealqrealqrealqreal -->
<h3 class="fn"><a name="rotate-3"></a><span class="type">void</span> QMatrix4x4::<span class="name">rotate</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>angle</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>x</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>y</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>z</i> = 0.0f )</h3>
<p>This is an overloaded function.</p>
<p>Multiplies this matrix by another that rotates coordinates through <i>angle</i> degrees about the vector (<i>x</i>, <i>y</i>, <i>z</i>).</p>
<p><b>See also </b><a href="qmatrix4x4.html#scale">scale</a>() and <a href="qmatrix4x4.html#translate">translate</a>().</p>
<!-- @@@rotate -->
<!-- $$$row[overload1]$$$rowint -->
<h3 class="fn"><a name="row"></a><span class="type"><a href="qvector4d.html">QVector4D</a></span> QMatrix4x4::<span class="name">row</span> ( <span class="type">int</span> <i>index</i> ) const</h3>
<p>Returns the elements of row <i>index</i> as a 4D vector.</p>
<p><b>See also </b><a href="qmatrix4x4.html#setRow">setRow</a>() and <a href="qmatrix4x4.html#column">column</a>().</p>
<!-- @@@row -->
<!-- $$$scale[overload1]$$$scaleconstQVector3D& -->
<h3 class="fn"><a name="scale"></a><span class="type">void</span> QMatrix4x4::<span class="name">scale</span> ( const <span class="type"><a href="qvector3d.html">QVector3D</a></span> & <i>vector</i> )</h3>
<p>Multiplies this matrix by another that scales coordinates by the components of <i>vector</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#translate">translate</a>() and <a href="qmatrix4x4.html#rotate">rotate</a>().</p>
<!-- @@@scale -->
<!-- $$$scale$$$scaleqrealqreal -->
<h3 class="fn"><a name="scale-2"></a><span class="type">void</span> QMatrix4x4::<span class="name">scale</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>x</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>y</i> )</h3>
<p>This is an overloaded function.</p>
<p>Multiplies this matrix by another that scales coordinates by the components <i>x</i>, and <i>y</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#translate">translate</a>() and <a href="qmatrix4x4.html#rotate">rotate</a>().</p>
<!-- @@@scale -->
<!-- $$$scale$$$scaleqrealqrealqreal -->
<h3 class="fn"><a name="scale-3"></a><span class="type">void</span> QMatrix4x4::<span class="name">scale</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>x</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>y</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>z</i> )</h3>
<p>This is an overloaded function.</p>
<p>Multiplies this matrix by another that scales coordinates by the components <i>x</i>, <i>y</i>, and <i>z</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#translate">translate</a>() and <a href="qmatrix4x4.html#rotate">rotate</a>().</p>
<!-- @@@scale -->
<!-- $$$scale$$$scaleqreal -->
<h3 class="fn"><a name="scale-4"></a><span class="type">void</span> QMatrix4x4::<span class="name">scale</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>factor</i> )</h3>
<p>This is an overloaded function.</p>
<p>Multiplies this matrix by another that scales coordinates by the given <i>factor</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#translate">translate</a>() and <a href="qmatrix4x4.html#rotate">rotate</a>().</p>
<!-- @@@scale -->
<!-- $$$setColumn[overload1]$$$setColumnintconstQVector4D& -->
<h3 class="fn"><a name="setColumn"></a><span class="type">void</span> QMatrix4x4::<span class="name">setColumn</span> ( <span class="type">int</span> <i>index</i>, const <span class="type"><a href="qvector4d.html">QVector4D</a></span> & <i>value</i> )</h3>
<p>Sets the elements of column <i>index</i> to the components of <i>value</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#column">column</a>() and <a href="qmatrix4x4.html#setRow">setRow</a>().</p>
<!-- @@@setColumn -->
<!-- $$$setRow[overload1]$$$setRowintconstQVector4D& -->
<h3 class="fn"><a name="setRow"></a><span class="type">void</span> QMatrix4x4::<span class="name">setRow</span> ( <span class="type">int</span> <i>index</i>, const <span class="type"><a href="qvector4d.html">QVector4D</a></span> & <i>value</i> )</h3>
<p>Sets the elements of row <i>index</i> to the components of <i>value</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#row">row</a>() and <a href="qmatrix4x4.html#setColumn">setColumn</a>().</p>
<!-- @@@setRow -->
<!-- $$$setToIdentity[overload1]$$$setToIdentity -->
<h3 class="fn"><a name="setToIdentity"></a><span class="type">void</span> QMatrix4x4::<span class="name">setToIdentity</span> ()</h3>
<p>Sets this matrix to the identity.</p>
<p><b>See also </b><a href="qmatrix4x4.html#isIdentity">isIdentity</a>().</p>
<!-- @@@setToIdentity -->
<!-- $$$toAffine[overload1]$$$toAffine -->
<h3 class="fn"><a name="toAffine"></a><span class="type"><a href="qmatrix.html">QMatrix</a></span> QMatrix4x4::<span class="name">toAffine</span> () const</h3>
<p>Returns the conventional Qt 2D affine transformation matrix that corresponds to this matrix. It is assumed that this matrix only contains 2D affine transformation elements.</p>
<p><b>See also </b><a href="qmatrix4x4.html#toTransform">toTransform</a>().</p>
<!-- @@@toAffine -->
<!-- $$$toGenericMatrix[overload1]$$$toGenericMatrix -->
<h3 class="fn"><a name="toGenericMatrix"></a><span class="type"><a href="qgenericmatrix.html">QGenericMatrix</a></span><<span class="type">N</span>, <span class="type">M</span>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span>> QMatrix4x4::<span class="name">toGenericMatrix</span> () const</h3>
<p>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.</p>
<!-- @@@toGenericMatrix -->
<!-- $$$toTransform[overload1]$$$toTransform -->
<h3 class="fn"><a name="toTransform"></a><span class="type"><a href="qtransform.html">QTransform</a></span> QMatrix4x4::<span class="name">toTransform</span> () const</h3>
<p>Returns the conventional Qt 2D transformation matrix that corresponds to this matrix.</p>
<p>The returned <a href="qtransform.html">QTransform</a> is formed by simply dropping the third row and third column of the <a href="qmatrix4x4.html">QMatrix4x4</a>. This is suitable for implementing orthographic projections where the z co-ordinate should be dropped rather than projected.</p>
<p><b>See also </b><a href="qmatrix4x4.html#toAffine">toAffine</a>().</p>
<!-- @@@toTransform -->
<!-- $$$toTransform$$$toTransformqreal -->
<h3 class="fn"><a name="toTransform-2"></a><span class="type"><a href="qtransform.html">QTransform</a></span> QMatrix4x4::<span class="name">toTransform</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>distanceToPlane</i> ) const</h3>
<p>Returns the conventional Qt 2D transformation matrix that corresponds to this matrix.</p>
<p>If <i>distanceToPlane</i> is non-zero, it indicates a projection factor to use to adjust for the z co-ordinate. The value of 1024 corresponds to the projection factor used by <a href="qtransform.html#rotate">QTransform::rotate</a>() for the x and y axes.</p>
<p>If <i>distanceToPlane</i> is zero, then the returned <a href="qtransform.html">QTransform</a> is formed by simply dropping the third row and third column of the <a href="qmatrix4x4.html">QMatrix4x4</a>. This is suitable for implementing orthographic projections where the z co-ordinate should be dropped rather than projected.</p>
<p><b>See also </b><a href="qmatrix4x4.html#toAffine">toAffine</a>().</p>
<!-- @@@toTransform -->
<!-- $$$translate[overload1]$$$translateconstQVector3D& -->
<h3 class="fn"><a name="translate"></a><span class="type">void</span> QMatrix4x4::<span class="name">translate</span> ( const <span class="type"><a href="qvector3d.html">QVector3D</a></span> & <i>vector</i> )</h3>
<p>Multiplies this matrix by another that translates coordinates by the components of <i>vector</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#scale">scale</a>() and <a href="qmatrix4x4.html#rotate">rotate</a>().</p>
<!-- @@@translate -->
<!-- $$$translate$$$translateqrealqreal -->
<h3 class="fn"><a name="translate-2"></a><span class="type">void</span> QMatrix4x4::<span class="name">translate</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>x</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>y</i> )</h3>
<p>This is an overloaded function.</p>
<p>Multiplies this matrix by another that translates coordinates by the components <i>x</i>, and <i>y</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#scale">scale</a>() and <a href="qmatrix4x4.html#rotate">rotate</a>().</p>
<!-- @@@translate -->
<!-- $$$translate$$$translateqrealqrealqreal -->
<h3 class="fn"><a name="translate-3"></a><span class="type">void</span> QMatrix4x4::<span class="name">translate</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>x</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>y</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>z</i> )</h3>
<p>This is an overloaded function.</p>
<p>Multiplies this matrix by another that translates coordinates by the components <i>x</i>, <i>y</i>, and <i>z</i>.</p>
<p><b>See also </b><a href="qmatrix4x4.html#scale">scale</a>() and <a href="qmatrix4x4.html#rotate">rotate</a>().</p>
<!-- @@@translate -->
<!-- $$$transposed[overload1]$$$transposed -->
<h3 class="fn"><a name="transposed"></a><span class="type">QMatrix4x4</span> QMatrix4x4::<span class="name">transposed</span> () const</h3>
<p>Returns this matrix, transposed about its diagonal.</p>
<!-- @@@transposed -->
<!-- $$$operator QVariant[overload1]$$$operator QVariant -->
<h3 class="fn"><a name="operator-QVariant"></a>QMatrix4x4::<span class="name">operator QVariant</span> () const</h3>
<p>Returns the matrix as a <a href="qvariant.html">QVariant</a>.</p>
<!-- @@@operator QVariant -->
<!-- $$$operator!=[overload1]$$$operator!=constQMatrix4x4& -->
<h3 class="fn"><a name="operator-not-eq"></a><span class="type">bool</span> QMatrix4x4::<span class="name">operator!=</span> ( const <span class="type">QMatrix4x4</span> & <i>other</i> ) const</h3>
<p>Returns true if this matrix is not identical to <i>other</i>; false otherwise. This operator uses an exact floating-point comparison.</p>
<!-- @@@operator!= -->
<!-- $$$operator()[overload1]$$$operator()intint -->
<h3 class="fn"><a name="operator-28-29"></a>const <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> & QMatrix4x4::<span class="name">operator()</span> ( <span class="type">int</span> <i>row</i>, <span class="type">int</span> <i>column</i> ) const</h3>
<p>Returns a constant reference to the element at position (<i>row</i>, <i>column</i>) in this matrix.</p>
<p><b>See also </b><a href="qmatrix4x4.html#column">column</a>() and <a href="qmatrix4x4.html#row">row</a>().</p>
<!-- @@@operator() -->
<!-- $$$operator()$$$operator()intint -->
<h3 class="fn"><a name="operator-28-29-2"></a><span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> & QMatrix4x4::<span class="name">operator()</span> ( <span class="type">int</span> <i>row</i>, <span class="type">int</span> <i>column</i> )</h3>
<p>Returns a reference to the element at position (<i>row</i>, <i>column</i>) in this matrix so that the element can be assigned to.</p>
<p><b>See also </b><a href="qmatrix4x4.html#optimize">optimize</a>(), <a href="qmatrix4x4.html#setColumn">setColumn</a>(), and <a href="qmatrix4x4.html#setRow">setRow</a>().</p>
<!-- @@@operator() -->
<!-- $$$operator*=[overload1]$$$operator*=constQMatrix4x4& -->
<h3 class="fn"><a name="operator-2a-eq"></a><span class="type">QMatrix4x4</span> & QMatrix4x4::<span class="name">operator*=</span> ( const <span class="type">QMatrix4x4</span> & <i>other</i> )</h3>
<p>Multiplies the contents of <i>other</i> by this matrix.</p>
<!-- @@@operator*= -->
<!-- $$$operator*=$$$operator*=qreal -->
<h3 class="fn"><a name="operator-2a-eq-2"></a><span class="type">QMatrix4x4</span> & QMatrix4x4::<span class="name">operator*=</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>factor</i> )</h3>
<p>This is an overloaded function.</p>
<p>Multiplies all elements of this matrix by <i>factor</i>.</p>
<!-- @@@operator*= -->
<!-- $$$operator+=[overload1]$$$operator+=constQMatrix4x4& -->
<h3 class="fn"><a name="operator-2b-eq"></a><span class="type">QMatrix4x4</span> & QMatrix4x4::<span class="name">operator+=</span> ( const <span class="type">QMatrix4x4</span> & <i>other</i> )</h3>
<p>Adds the contents of <i>other</i> to this matrix.</p>
<!-- @@@operator+= -->
<!-- $$$operator-=[overload1]$$$operator-=constQMatrix4x4& -->
<h3 class="fn"><a name="operator--eq"></a><span class="type">QMatrix4x4</span> & QMatrix4x4::<span class="name">operator-=</span> ( const <span class="type">QMatrix4x4</span> & <i>other</i> )</h3>
<p>Subtracts the contents of <i>other</i> from this matrix.</p>
<!-- @@@operator-= -->
<!-- $$$operator/=[overload1]$$$operator/=qreal -->
<h3 class="fn"><a name="operator-2f-eq"></a><span class="type">QMatrix4x4</span> & QMatrix4x4::<span class="name">operator/=</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>divisor</i> )</h3>
<p>This is an overloaded function.</p>
<p>Divides all elements of this matrix by <i>divisor</i>.</p>
<!-- @@@operator/= -->
<!-- $$$operator==[overload1]$$$operator==constQMatrix4x4& -->
<h3 class="fn"><a name="operator-eq-eq"></a><span class="type">bool</span> QMatrix4x4::<span class="name">operator==</span> ( const <span class="type">QMatrix4x4</span> & <i>other</i> ) const</h3>
<p>Returns true if this matrix is identical to <i>other</i>; false otherwise. This operator uses an exact floating-point comparison.</p>
<!-- @@@operator== -->
</div>
<div class="relnonmem">
<h2>Related Non-Members</h2>
<!-- $$$qFuzzyCompare$$$qFuzzyCompareconstQMatrix4x4&constQMatrix4x4& -->
<h3 class="fn"><a name="qFuzzyCompare-2"></a><span class="type">bool</span> <span class="name">qFuzzyCompare</span> ( const <span class="type">QMatrix4x4</span> & <i>m1</i>, const <span class="type">QMatrix4x4</span> & <i>m2</i> )</h3>
<p>Returns true if <i>m1</i> and <i>m2</i> are equal, allowing for a small fuzziness factor for floating-point comparisons; false otherwise.</p>
<!-- @@@qFuzzyCompare -->
<!-- $$$operator*$$$operator*constQMatrix4x4&constQMatrix4x4& -->
<h3 class="fn"><a name="operator-2a-4"></a><span class="type">QMatrix4x4</span> <span class="name">operator*</span> ( const <span class="type">QMatrix4x4</span> & <i>m1</i>, const <span class="type">QMatrix4x4</span> & <i>m2</i> )</h3>
<p>Returns the product of <i>m1</i> and <i>m2</i>.</p>
<!-- @@@operator* -->
<!-- $$$operator*$$$operator*constQVector3D&constQMatrix4x4& -->
<h3 class="fn"><a name="operator-2a-5"></a><span class="type"><a href="qvector3d.html">QVector3D</a></span> <span class="name">operator*</span> ( const <span class="type"><a href="qvector3d.html">QVector3D</a></span> & <i>vector</i>, const <span class="type">QMatrix4x4</span> & <i>matrix</i> )</h3>
<p>Returns the result of transforming <i>vector</i> according to <i>matrix</i>, with the matrix applied post-vector.</p>
<!-- @@@operator* -->
<!-- $$$operator*$$$operator*constQMatrix4x4&constQVector3D& -->
<h3 class="fn"><a name="operator-2a-6"></a><span class="type"><a href="qvector3d.html">QVector3D</a></span> <span class="name">operator*</span> ( const <span class="type">QMatrix4x4</span> & <i>matrix</i>, const <span class="type"><a href="qvector3d.html">QVector3D</a></span> & <i>vector</i> )</h3>
<p>Returns the result of transforming <i>vector</i> according to <i>matrix</i>, with the matrix applied pre-vector.</p>
<!-- @@@operator* -->
<!-- $$$operator*$$$operator*constQVector4D&constQMatrix4x4& -->
<h3 class="fn"><a name="operator-2a-7"></a><span class="type"><a href="qvector4d.html">QVector4D</a></span> <span class="name">operator*</span> ( const <span class="type"><a href="qvector4d.html">QVector4D</a></span> & <i>vector</i>, const <span class="type">QMatrix4x4</span> & <i>matrix</i> )</h3>
<p>Returns the result of transforming <i>vector</i> according to <i>matrix</i>, with the matrix applied post-vector.</p>
<!-- @@@operator* -->
<!-- $$$operator*$$$operator*constQMatrix4x4&constQVector4D& -->
<h3 class="fn"><a name="operator-2a-8"></a><span class="type"><a href="qvector4d.html">QVector4D</a></span> <span class="name">operator*</span> ( const <span class="type">QMatrix4x4</span> & <i>matrix</i>, const <span class="type"><a href="qvector4d.html">QVector4D</a></span> & <i>vector</i> )</h3>
<p>Returns the result of transforming <i>vector</i> according to <i>matrix</i>, with the matrix applied pre-vector.</p>
<!-- @@@operator* -->
<!-- $$$operator*$$$operator*constQPoint&constQMatrix4x4& -->
<h3 class="fn"><a name="operator-2a-9"></a><span class="type"><a href="qpoint.html">QPoint</a></span> <span class="name">operator*</span> ( const <span class="type"><a href="qpoint.html">QPoint</a></span> & <i>point</i>, const <span class="type">QMatrix4x4</span> & <i>matrix</i> )</h3>
<p>Returns the result of transforming <i>point</i> according to <i>matrix</i>, with the matrix applied post-point.</p>
<!-- @@@operator* -->
<!-- $$$operator*$$$operator*constQPointF&constQMatrix4x4& -->
<h3 class="fn"><a name="operator-2a-10"></a><span class="type"><a href="qpointf.html">QPointF</a></span> <span class="name">operator*</span> ( const <span class="type"><a href="qpointf.html">QPointF</a></span> & <i>point</i>, const <span class="type">QMatrix4x4</span> & <i>matrix</i> )</h3>
<p>Returns the result of transforming <i>point</i> according to <i>matrix</i>, with the matrix applied post-point.</p>
<!-- @@@operator* -->
<!-- $$$operator*$$$operator*constQMatrix4x4&constQPoint& -->
<h3 class="fn"><a name="operator-2a-11"></a><span class="type"><a href="qpoint.html">QPoint</a></span> <span class="name">operator*</span> ( const <span class="type">QMatrix4x4</span> & <i>matrix</i>, const <span class="type"><a href="qpoint.html">QPoint</a></span> & <i>point</i> )</h3>
<p>Returns the result of transforming <i>point</i> according to <i>matrix</i>, with the matrix applied pre-point.</p>
<!-- @@@operator* -->
<!-- $$$operator*$$$operator*constQMatrix4x4&constQPointF& -->
<h3 class="fn"><a name="operator-2a-12"></a><span class="type"><a href="qpointf.html">QPointF</a></span> <span class="name">operator*</span> ( const <span class="type">QMatrix4x4</span> & <i>matrix</i>, const <span class="type"><a href="qpointf.html">QPointF</a></span> & <i>point</i> )</h3>
<p>Returns the result of transforming <i>point</i> according to <i>matrix</i>, with the matrix applied pre-point.</p>
<!-- @@@operator* -->
<!-- $$$operator*$$$operator*qrealconstQMatrix4x4& -->
<h3 class="fn"><a name="operator-2a-13"></a><span class="type">QMatrix4x4</span> <span class="name">operator*</span> ( <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>factor</i>, const <span class="type">QMatrix4x4</span> & <i>matrix</i> )</h3>
<p>Returns the result of multiplying all elements of <i>matrix</i> by <i>factor</i>.</p>
<!-- @@@operator* -->
<!-- $$$operator*$$$operator*constQMatrix4x4&qreal -->
<h3 class="fn"><a name="operator-2a-14"></a><span class="type">QMatrix4x4</span> <span class="name">operator*</span> ( const <span class="type">QMatrix4x4</span> & <i>matrix</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>factor</i> )</h3>
<p>Returns the result of multiplying all elements of <i>matrix</i> by <i>factor</i>.</p>
<!-- @@@operator* -->
<!-- $$$operator+$$$operator+constQMatrix4x4&constQMatrix4x4& -->
<h3 class="fn"><a name="operator-2b-2"></a><span class="type">QMatrix4x4</span> <span class="name">operator+</span> ( const <span class="type">QMatrix4x4</span> & <i>m1</i>, const <span class="type">QMatrix4x4</span> & <i>m2</i> )</h3>
<p>Returns the sum of <i>m1</i> and <i>m2</i>.</p>
<!-- @@@operator+ -->
<!-- $$$operator-$$$operator-constQMatrix4x4&constQMatrix4x4& -->
<h3 class="fn"><a name="operator--2"></a><span class="type">QMatrix4x4</span> <span class="name">operator-</span> ( const <span class="type">QMatrix4x4</span> & <i>m1</i>, const <span class="type">QMatrix4x4</span> & <i>m2</i> )</h3>
<p>Returns the difference of <i>m1</i> and <i>m2</i>.</p>
<!-- @@@operator- -->
<!-- $$$operator-$$$operator-constQMatrix4x4& -->
<h3 class="fn"><a name="operator--24"></a><span class="type">QMatrix4x4</span> <span class="name">operator-</span> ( const <span class="type">QMatrix4x4</span> & <i>matrix</i> )</h3>
<p>This is an overloaded function.</p>
<p>Returns the negation of <i>matrix</i>.</p>
<!-- @@@operator- -->
<!-- $$$operator/$$$operator/constQMatrix4x4&qreal -->
<h3 class="fn"><a name="operator-2f-2"></a><span class="type">QMatrix4x4</span> <span class="name">operator/</span> ( const <span class="type">QMatrix4x4</span> & <i>matrix</i>, <span class="type"><a href="qtglobal.html#qreal-typedef">qreal</a></span> <i>divisor</i> )</h3>
<p>Returns the result of dividing all elements of <i>matrix</i> by <i>divisor</i>.</p>
<!-- @@@operator/ -->
<!-- $$$operator<<$$$operator<<QDataStream&constQMatrix4x4& -->
<h3 class="fn"><a name="operator-lt-lt-25"></a><span class="type"><a href="qdatastream.html">QDataStream</a></span> & <span class="name">operator<<</span> ( <span class="type"><a href="qdatastream.html">QDataStream</a></span> & <i>stream</i>, const <span class="type">QMatrix4x4</span> & <i>matrix</i> )</h3>
<p>Writes the given <i>matrix</i> to the given <i>stream</i> and returns a reference to the stream.</p>
<p><b>See also </b><a href="datastreamformat.html">Serializing Qt Data Types</a>.</p>
<!-- @@@operator<< -->
<!-- $$$operator>>$$$operator>>QDataStream&QMatrix4x4& -->
<h3 class="fn"><a name="operator-gt-gt-15"></a><span class="type"><a href="qdatastream.html">QDataStream</a></span> & <span class="name">operator>></span> ( <span class="type"><a href="qdatastream.html">QDataStream</a></span> & <i>stream</i>, <span class="type">QMatrix4x4</span> & <i>matrix</i> )</h3>
<p>Reads a 4x4 matrix from the given <i>stream</i> into the given <i>matrix</i> and returns a reference to the stream.</p>
<p><b>See also </b><a href="datastreamformat.html">Serializing Qt Data Types</a>.</p>
<!-- @@@operator>> -->
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