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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"><html><head><meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Qt Toolkit - QWMatrix Class</title><style type="text/css"><!--
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<h1 align=center>QWMatrix Class Reference</h1><br clear="all">
<p>
The QWMatrix class specifies 2D transformations of a coordinate system.
<a href="#details">More...</a>
<p>
<code>#include <<a href="qwmatrix-h.html">qwmatrix.h</a>></code>
<p><a href="qwmatrix-members.html">List of all member functions.</a>
<h2>Public Members</h2>
<ul>
<li><div class="fn"><a href="#5b24cf"><b>QWMatrix</b></a>()</div>
<li><div class="fn"><a href="#1ee86a"><b>QWMatrix</b></a>(doublem11, doublem12, doublem21, doublem22, doubledx, doubledy)</div>
<li><div class="fn">void<a href="#758626"><b>setMatrix</b></a>(doublem11, doublem12, doublem21, doublem22, doubledx, doubledy)</div>
<li><div class="fn">double<a href="#b24a8d"><b>m11</b></a>()const</div>
<li><div class="fn">double<a href="#f60706"><b>m12</b></a>()const</div>
<li><div class="fn">double<a href="#3da1aa"><b>m21</b></a>()const</div>
<li><div class="fn">double<a href="#5ceba1"><b>m22</b></a>()const</div>
<li><div class="fn">double<a href="#58f7fe"><b>dx</b></a>()const</div>
<li><div class="fn">double<a href="#600479"><b>dy</b></a>()const</div>
<li><div class="fn">void<a href="#c5581f"><b>map</b></a>(intx, inty, int*tx, int*ty)const</div>
<li><div class="fn">void<a href="#83c725"><b>map</b></a>(doublex, doubley, double*tx, double*ty)const</div>
<li><div class="fn">QPoint<a href="#fe18db"><b>map</b></a>(constQPoint&)const</div>
<li><div class="fn">QRect<a href="#a5969f"><b>map</b></a>(constQRect&)const</div>
<li><div class="fn">QPointArray<a href="#95bc92"><b>map</b></a>(constQPointArray&)const</div>
<li><div class="fn">void<a href="#e13f59"><b>reset</b></a>()</div>
<li><div class="fn">QWMatrix&<a href="#e4b716"><b>translate</b></a>(doubledx, doubledy)</div>
<li><div class="fn">QWMatrix&<a href="#41a356"><b>scale</b></a>(doublesx, doublesy)</div>
<li><div class="fn">QWMatrix&<a href="#b99fbb"><b>shear</b></a>(doublesh, doublesv)</div>
<li><div class="fn">QWMatrix&<a href="#71020d"><b>rotate</b></a>(doublea)</div>
<li><div class="fn">QWMatrix<a href="#4b7815"><b>invert</b></a>(bool*=0)const</div>
<li><div class="fn">bool<a href="#1a89f8"><b>operator==</b></a>(constQWMatrix&)const</div>
<li><div class="fn">bool<a href="#4d0879"><b>operator!=</b></a>(constQWMatrix&)const</div>
<li><div class="fn">QWMatrix&<a href="#9915db"><b>operator*=</b></a>(constQWMatrix&)</div>
</ul>
<h2>Related Functions</h2>
(Note that these are not member functions.)
<ul>
<li>QDataStream & <a href="qwmatrix.html#52be3f"><b>operator>></b></a> (QDataStream & s, QWMatrix & m)
<li>QDataStream & <a href="qwmatrix.html#d68356"><b>operator<<</b></a> (QDataStream & s, const QWMatrix & m)
<li>QWMatrix <a href="qwmatrix.html#e3021d"><b>operator*</b></a> (const QWMatrix & m1, const QWMatrix & m2)
</ul>
<hr><h2><a name="details"></a>Detailed Description</h2>
The QWMatrix class specifies 2D transformations of a coordinate system.
<p>
The standard coordinate system of a <a href="qpaintdevice.html">paint
device</a> has the origin located at the top left position. X
values increase to the right, and Y values increase downwards.
<p>This coordinate system is default for the <a href="qpainter.html">QPainter</a>, which renders
graphics in a paint device. A user-defined coordinate system can be
specified by setting a QWMatrix for the painter.
<p>Example:
<pre> MyWidget::paintEvent( <a href="qpaintevent.html">QPaintEvent</a> * )
{
<a href="qpainter.html">QPainter</a> p; // our painter
<a href="qwmatrix.html">QWMatrix</a> m; // our transformation matrix
m.<a href="#71020d">rotate</a>( 22.5 ); // rotated coordinate system
p.<a href="qpainter.html#02ed5d">begin</a>( this ); // start painting
p.<a href="qpainter.html#862c4d">setWorldMatrix</a>( m ); // use rotated coordinate system
p.<a href="qpainter.html#0f088f">drawText</a>( 30,20, "detator" ); // draw rotated text at 30,20
p.<a href="qpainter.html#365784">end</a>(); // painting done
}
</pre>
<p>A matrix specifies how to translate, scale, shear or rotate the
graphics, and the actual transformation is performed by the drawing
routines in QPainter and by <a href="qpixmap.html#ff5fcf">QPixmap::xForm</a>().
<p>The QWMatrix class contains a 3*3 matrix of the form:
<pre>
m11 m12 0
m21 m22 0
dx dy 1
</pre>
<p>A matrix transforms a point in the plane to another point:
<pre> x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy
</pre>
<p>The point <em>(x,y)</em> is the original point, and <em>(x',y')</em> is the
transformed point. <em>(x',y')</em> can be transformed back to <em>(x,y)</em>
by performing the same operation on the <a href="#4b7815">inverted matrix</a>.
<p>The elements <em>dx</em> and <em>dy</em> specify horisontal and vertical
translation. The elements <em>m11</em> and <em>m22</em> specify horisontal and
vertical scaling. The elements <em>m12</em> and <em>m21</em> specify horisontal
and vertical shearing.
<p>The identity matrix has <em>m11</em> and <em>m22</em> set to 1, all others set
to 0. This matrix maps a point to itself.
<p>Translation is the simplest transformation. Setting <em>dx</em> and <em>dy</em>
will move the coordinate system <em>dx</em> units along the X axis and <em>dy</em> units along the Y axis.
<p>Scaling can be done by setting <em>m11</em> and <em>m22.</em> For example,
setting <em>m11</em> to 2 and <em>m22</em> to 1.5 will double the height and
increase the width by 50%.
<p>Shearing is controlled by <em>m12</em> and <em>m21.</em> Setting these elements
to values different from zero will twist the coordinate system.
<p>Rotation is achieved by carefully setting both the shearing factors
and the scaling factors. The QWMatrix has a function that sets
<a href="#71020d">rotation</a> directly.
<p>QWMatrix lets you combine transformations like this:
<pre> <a href="qwmatrix.html">QWMatrix</a> m; // identity matrix
m.<a href="#e4b716">translate</a>(10, -20); // first translate (10,-20)
m.<a href="#71020d">rotate</a>(25); // then rotate 25 degrees
m.<a href="#41a356">scale</a>(1.2, 0.7); // finally scale it
</pre>
<p>The same example, but using basic matrix operations:
<pre> double a = pi/180 * 25; // convert 25 to radians
double sina = sin(a);
double cosa = cos(a);
<a href="qwmatrix.html">QWMatrix</a> m1(0, 0, 0, 0, 10, -20); // translation matrix
<a href="qwmatrix.html">QWMatrix</a> m2( cosa, sina, // rotation matrix
-sina, cosa, 0, 0 );
<a href="qwmatrix.html">QWMatrix</a> m3(1.2, 0, 0, 0.7, 0, 0); // scaling matrix
<a href="qwmatrix.html">QWMatrix</a> m;
m = m3 * m2 * m1; // combine all transformations
</pre>
<p><a href="qpainter.html">QPainter</a> has functions that <a href="qpainter.html#eb778c">translate</a>, <a href="qpainter.html#e5ec3e">scale</a>, <a href="qpainter.html#c8634b">shear</a> and <a href="qpainter.html#b5205c">rotate</a> the coordinate system without using a
QWMatrix. These functions are very convenient, however, if you want to
perform more than a single transform operation, it is more efficient to
build a QWMatrix and call <a href="qpainter.html#862c4d">QPainter::setWorldMatrix</a>().
<p>See also <a href="qpainter.html#862c4d">QPainter::setWorldMatrix</a>() and <a href="qpixmap.html#ff5fcf">QPixmap::xForm</a>().
<p>Examples:
<a href="qtimage-qtimage-cpp.html#QWMatrix">qtimage/qtimage.cpp</a>
<a href="xform-xform-cpp.html#QWMatrix">xform/xform.cpp</a>
<a href="drawdemo-drawdemo-cpp.html#QWMatrix">drawdemo/drawdemo.cpp</a>
<a href="qmag-qmag-cpp.html#QWMatrix">qmag/qmag.cpp</a>
<a href="desktop-desktop-cpp.html#QWMatrix">desktop/desktop.cpp</a>
<a href="movies-main-cpp.html#QWMatrix">movies/main.cpp</a>
<hr><h2>Member Function Documentation</h2>
<h3 class="fn"><a name="5b24cf"></a>QWMatrix::QWMatrix()</h3>
<p>Constructs an identity matrix. All elements are set to zero,
except <em>m11</em> and <em>m22</em> (scaling) which are set to 1.
<h3 class="fn"><a name="1ee86a"></a>QWMatrix::QWMatrix(doublem11, doublem12, doublem21, doublem22, doubledx, doubledy)</h3>
<p>Constructs a matrix with the specified elements.
<h3 class="fn">double<a name="58f7fe"></a>QWMatrix::dx()const</h3>
<p>Returns the horizontal translation.
<h3 class="fn">double<a name="600479"></a>QWMatrix::dy()const</h3>
<p>Returns the vertical translation.
<h3 class="fn">QWMatrix<a name="4b7815"></a>QWMatrix::invert(bool*invertible=0)const</h3>
<p>Returns the inverted matrix.
<p>If the matrix is singular (not invertible), then the identity matrix is
returned.
<p>If <em>*invertible</em> is not null, then the value of <em>*invertible</em> will
be set to TRUE or FALSE to tell if the matrix is invertible or not.
<h3 class="fn">double<a name="b24a8d"></a>QWMatrix::m11()const</h3>
<p>Returns the X scaling factor.
<h3 class="fn">double<a name="f60706"></a>QWMatrix::m12()const</h3>
<p>Returns the vertical shearing factor.
<h3 class="fn">double<a name="3da1aa"></a>QWMatrix::m21()const</h3>
<p>Returns the horizontal shearing factor.
<h3 class="fn">double<a name="5ceba1"></a>QWMatrix::m22()const</h3>
<p>Returns the Y scaling factor.
<h3 class="fn"><a href="qpoint.html">QPoint</a><a name="fe18db"></a>QWMatrix::map(const<a href="qpoint.html">QPoint</a>&p)const</h3>
<p>Returns the transformed <em>p.</em>
<h3 class="fn"><a href="qpointarray.html">QPointArray</a><a name="95bc92"></a>QWMatrix::map(const<a href="qpointarray.html">QPointArray</a>&a)const</h3>
<p>Returns the point array <em>a</em> transformed by calling map for each point.
<h3 class="fn"><a href="qrect.html">QRect</a><a name="a5969f"></a>QWMatrix::map(const<a href="qrect.html">QRect</a>&r)const</h3>
<p>Returns the transformed rectangle <em>r.</em>
<p>If rotation or shearing has been specified, then the bounding rectangle
will be returned.
<h3 class="fn">void<a name="83c725"></a>QWMatrix::map(doublex, doubley, double*tx, double*ty)const</h3>
<p>Transforms <em>(x,y)</em> to <em>(*tx,*ty),</em> using the formulae:
<p><pre> *tx = m11*x + m21*y + dx
*ty = m22*y + m12*x + dy
</pre>
<p>Examples:
<a href="xform-xform-cpp.html#map">xform/xform.cpp</a>
<h3 class="fn">void<a name="c5581f"></a>QWMatrix::map(intx, inty, int*tx, int*ty)const</h3>
<p>Transforms <em>(x,y)</em> to <em>(*tx,*ty),</em> using the formulae:
<p><pre> *tx = m11*x + m21*y + dx -- (rounded to the nearest integer)
*ty = m22*y + m12*x + dy -- (rounded to the nearest integer)
</pre>
<h3 class="fn">bool<a name="4d0879"></a>QWMatrix::operator!=(constQWMatrix&m)const</h3>
<p>Returns TRUE if this matrix is not equal to <em>m.</em>
<h3 class="fn">QWMatrix&<a name="9915db"></a>QWMatrix::operator*=(constQWMatrix&m)</h3>
<p>Returns the result of multiplying this matrix with <em>m.</em>
<h3 class="fn">bool<a name="1a89f8"></a>QWMatrix::operator==(constQWMatrix&m)const</h3>
<p>Returns TRUE if this matrix is equal to <em>m.</em>
<h3 class="fn">void<a name="e13f59"></a>QWMatrix::reset()</h3>
<p>Resets the matrix to an identity matrix.
<p>All elements are set to zero, except <em>m11</em> and <em>m22</em> (scaling)
that are set to 1.
<h3 class="fn">QWMatrix&<a name="71020d"></a>QWMatrix::rotate(doublea)</h3>
<p>Rotates the coordinate system <em>a</em> degrees counterclockwise.
<p>Returns a reference to the matrix.
<p>See also <a href="#e4b716">translate</a>(), <a href="#41a356">scale</a>() and <a href="#b99fbb">shear</a>().
<p>Examples:
<a href="xform-xform-cpp.html#rotate">xform/xform.cpp</a>
<a href="drawdemo-drawdemo-cpp.html#rotate">drawdemo/drawdemo.cpp</a>
<a href="desktop-desktop-cpp.html#rotate">desktop/desktop.cpp</a>
<h3 class="fn">QWMatrix&<a name="41a356"></a>QWMatrix::scale(doublesx, doublesy)</h3>
<p>Scales the coordinate system unit by <em>sx</em> horizontally and <em>sy</em>
vertically.
<p>Returns a reference to the matrix.
<p>See also <a href="#e4b716">translate</a>(), <a href="#b99fbb">shear</a>() and <a href="#71020d">rotate</a>().
<p>Examples:
<a href="qtimage-qtimage-cpp.html#scale">qtimage/qtimage.cpp</a>
<a href="xform-xform-cpp.html#scale">xform/xform.cpp</a>
<a href="movies-main-cpp.html#scale">movies/main.cpp</a>
<h3 class="fn">void<a name="758626"></a>QWMatrix::setMatrix(doublem11, doublem12, doublem21, doublem22, doubledx, doubledy)</h3>
<p>Sets the matrix elements to the specified values.
<h3 class="fn">QWMatrix&<a name="b99fbb"></a>QWMatrix::shear(doublesh, doublesv)</h3>
<p>Shears the coordinate system by <em>sh</em> horizontally and <em>sv</em> vertically.
<p>Returns a reference to the matrix.
<p>See also <a href="#e4b716">translate</a>(), <a href="#41a356">scale</a>() and <a href="#71020d">rotate</a>().
<p>Examples:
<a href="xform-xform-cpp.html#shear">xform/xform.cpp</a>
<a href="drawdemo-drawdemo-cpp.html#shear">drawdemo/drawdemo.cpp</a>
<h3 class="fn">QWMatrix&<a name="e4b716"></a>QWMatrix::translate(doubledx, doubledy)</h3>
<p>Moves the coordinate system <em>dx</em> along the X-axis and <em>dy</em>
along the Y-axis.
<p>Returns a reference to the matrix.
<p>See also <a href="#41a356">scale</a>(), <a href="#b99fbb">shear</a>() and <a href="#71020d">rotate</a>().
<p>Examples:
<a href="xform-xform-cpp.html#translate">xform/xform.cpp</a>
<a href="drawdemo-drawdemo-cpp.html#translate">drawdemo/drawdemo.cpp</a>
<hr><h2>Related Functions</h2>
<h3><a href="qdatastream.html">QDataStream</a> & <a name="52be3f"></a>operator>> (<a href="qdatastream.html">QDataStream</a> & s, QWMatrix & m)</h3>
<p>Reads a matrix from the stream and returns a reference to the stream.
<p>See also <a href="datastreamformat.html">Format of the QDataStream operators</a>
<h3><a href="qdatastream.html">QDataStream</a> & <a name="d68356"></a>operator<< (<a href="qdatastream.html">QDataStream</a> & s, const QWMatrix & m)</h3>
<p>Writes a matrix to the stream and returns a reference to the stream.
<p>See also <a href="datastreamformat.html">Format of the QDataStream operators</a>
<h3>QWMatrix <a name="e3021d"></a>operator* (const QWMatrix & m1, const QWMatrix & m2)</h3>
<p>Returns the product <em>m1</em> * <em>m2.</em>
<p>Remember that matrix multiplication is not commutative, thus
a*b != b*a.
<hr><p>
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