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<td align="right" valign="center"><img src="logo32.png" align="right" width="64" height="32" border="0"></td></tr></table><h1 align=center>QWMatrix Class Reference</h1>
<p>The QWMatrix class specifies 2D transformations of a
coordinate system.
<a href="#details">More...</a>
<p><tt>#include <<a href="qwmatrix-h.html">qwmatrix.h</a>></tt>
<p><a href="qwmatrix-members.html">List of all member functions.</a>
<h2>Public Members</h2>
<ul>
<li><div class=fn><a href="#QWMatrix"><b>QWMatrix</b></a> ()</div></li>
<li><div class=fn><a href="#QWMatrix-2"><b>QWMatrix</b></a> ( double m11, double m12, double m21, double m22, double dx, double dy )</div></li>
<li><div class=fn>void <a href="#setMatrix"><b>setMatrix</b></a> ( double m11, double m12, double m21, double m22, double dx, double dy )</div></li>
<li><div class=fn>double <a href="#m11"><b>m11</b></a> () const</div></li>
<li><div class=fn>double <a href="#m12"><b>m12</b></a> () const</div></li>
<li><div class=fn>double <a href="#m21"><b>m21</b></a> () const</div></li>
<li><div class=fn>double <a href="#m22"><b>m22</b></a> () const</div></li>
<li><div class=fn>double <a href="#dx"><b>dx</b></a> () const</div></li>
<li><div class=fn>double <a href="#dy"><b>dy</b></a> () const</div></li>
<li><div class=fn>void <a href="#map"><b>map</b></a> ( int x, int y, int * tx, int * ty ) const</div></li>
<li><div class=fn>void <a href="#map-2"><b>map</b></a> ( double x, double y, double * tx, double * ty ) const</div></li>
<li><div class=fn>QRect <a href="#mapRect"><b>mapRect</b></a> ( const QRect & rect ) const</div></li>
<li><div class=fn>QPoint map ( const QPoint & p ) const <em>(obsolete)</em></div></li>
<li><div class=fn>QRect map ( const QRect & r ) const <em>(obsolete)</em></div></li>
<li><div class=fn>QPointArray map ( const QPointArray & a ) const <em>(obsolete)</em></div></li>
<li><div class=fn>void <a href="#reset"><b>reset</b></a> ()</div></li>
<li><div class=fn>bool <a href="#isIdentity"><b>isIdentity</b></a> () const</div></li>
<li><div class=fn>QWMatrix & <a href="#translate"><b>translate</b></a> ( double dx, double dy )</div></li>
<li><div class=fn>QWMatrix & <a href="#scale"><b>scale</b></a> ( double sx, double sy )</div></li>
<li><div class=fn>QWMatrix & <a href="#shear"><b>shear</b></a> ( double sh, double sv )</div></li>
<li><div class=fn>QWMatrix & <a href="#rotate"><b>rotate</b></a> ( double a )</div></li>
<li><div class=fn>bool <a href="#isInvertible"><b>isInvertible</b></a> () const</div></li>
<li><div class=fn>QWMatrix <a href="#invert"><b>invert</b></a> ( bool * invertible = 0 ) const</div></li>
<li><div class=fn>bool <a href="#operator-eq-eq"><b>operator==</b></a> ( const QWMatrix & m ) const</div></li>
<li><div class=fn>bool <a href="#operator!-eq"><b>operator!=</b></a> ( const QWMatrix & m ) const</div></li>
<li><div class=fn>QWMatrix & <a href="#operator*-eq"><b>operator*=</b></a> ( const QWMatrix & m )</div></li>
<li><div class=fn>QPoint <a href="#operator*"><b>operator*</b></a> ( const QPoint & p ) const</div></li>
<li><div class=fn>QRegion <a href="#operator*-2"><b>operator*</b></a> ( const QRect & r ) const</div></li>
<li><div class=fn>QRegion <a href="#operator*-3"><b>operator*</b></a> ( const QRegion & r ) const</div></li>
<li><div class=fn>QPointArray <a href="#operator*-4"><b>operator*</b></a> ( const QPointArray & a ) const</div></li>
</ul>
<h2>Related Functions</h2>
<ul>
<li><div class=fn>QWMatrix <a href="#operator*-5"><b>operator*</b></a> ( const QWMatrix & m1, const QWMatrix & m2 )</div></li>
<li><div class=fn>QDataStream & <a href="#operator-lt-lt"><b>operator<<</b></a> ( QDataStream & s, const QWMatrix & m )</div></li>
<li><div class=fn>QDataStream & <a href="#operator-gt-gt"><b>operator>></b></a> ( QDataStream & s, QWMatrix & m )</div></li>
</ul>
<hr><a name="details"></a><h2>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; Y values increase downward.
<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
QWMatrix m; // our transformation matrix
m.<a href="#rotate">rotate</a>( 22.5 ); // rotated coordinate system
p.<a href="qpainter.html#begin">begin</a>( this ); // start painting
p.<a href="qpainter.html#setWorldMatrix">setWorldMatrix</a>( m ); // use rotated coordinate system
p.<a href="qpainter.html#drawText">drawText</a>( 30,20, "detator" ); // draw rotated text at 30,20
p.<a href="qpainter.html#end">end</a>(); // painting done
}
</pre>
<p> A matrix specifies how to translate, scale, shear or rotate the
graphics; the actual transformation is performed by the drawing
routines in <a href="qpainter.html">QPainter</a> and by <a href="qpixmap.html#xForm">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="#invert">inverted matrix</a>.
<p> The elements <em>dx</em> and <em>dy</em> specify horizontal and vertical
translation. The elements <em>m11</em> and <em>m22</em> specify horizontal and
vertical scaling. The elements <em>m12</em> and <em>m21</em> specify horizontal and
vertical shearing.
<p> The identity matrix has <em>m11</em> and <em>m22</em> set to 1; all others are 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="#rotate">rotation</a> directly.
<p> QWMatrix lets you combine transformations like this:
<pre>
QWMatrix m; // identity matrix
m.<a href="#translate">translate</a>(10, -20); // first translate (10,-20)
m.<a href="#rotate">rotate</a>(25); // then rotate 25 degrees
m.<a href="#scale">scale</a>(1.2, 0.7); // finally scale it
</pre>
<p> Here's the same example using basic matrix operations:
<pre>
double a = pi/180 * 25; // convert 25 to radians
double sina = sin(a);
double cosa = cos(a);
QWMatrix m1(0, 0, 0, 0, 10, -20); // translation matrix
QWMatrix m2( cosa, sina, // rotation matrix
-sina, cosa, 0, 0 );
QWMatrix m3(1.2, 0, 0, 0.7, 0, 0); // scaling matrix
QWMatrix m;
m = m3 * m2 * m1; // combine all transformations
</pre>
<p> <a href="qpainter.html">QPainter</a> has functions to translate, scale, shear and rotate the
coordinate system without using a QWMatrix. Although these
functions are very convenient, it can be more efficient to build a
QWMatrix and call <a href="qpainter.html#setWorldMatrix">QPainter::setWorldMatrix</a>() if you want to perform
more than a single transform operation.
<p> <p>See also <a href="qpainter.html#setWorldMatrix">QPainter::setWorldMatrix</a>(), <a href="qpixmap.html#xForm">QPixmap::xForm</a>(), <a href="graphics.html">Graphics Classes</a> and <a href="images.html">Image Processing Classes</a>.
<hr><h2>Member Function Documentation</h2>
<h3 class=fn><a name="QWMatrix"></a>QWMatrix::QWMatrix ()
</h3>
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="QWMatrix-2"></a>QWMatrix::QWMatrix ( double m11, double m12, double m21, double m22, double dx, double dy )
</h3>
Constructs a matrix with the elements, <em>m11</em>, <em>m12</em>, <em>m21</em>, <em>m22</em>, <em>dx</em> and <em>dy</em>.
<h3 class=fn>double <a name="dx"></a>QWMatrix::dx () const
</h3>
<p> Returns the horizontal translation.
<h3 class=fn>double <a name="dy"></a>QWMatrix::dy () const
</h3>
<p> Returns the vertical translation.
<h3 class=fn><a href="qwmatrix.html">QWMatrix</a> <a name="invert"></a>QWMatrix::invert ( bool * invertible = 0 ) const
</h3>
Returns the inverted matrix.
<p> If the matrix is singular (not invertible), the identity matrix is
returned.
<p> If <em>invertible</em> is not null, the value of <em>*invertible</em> is set
to TRUE if the matrix is invertible or to FALSE if the matrix is
not invertible.
<p> <p>See also <a href="#isInvertible">isInvertible</a>().
<p>Example: <a href="t14.html#x2246">t14/cannon.cpp</a>.
<h3 class=fn>bool <a name="isIdentity"></a>QWMatrix::isIdentity () const
</h3>
Returns TRUE if the matrix is the identity matrix; otherwise returns FALSE.
<p> <p>See also <a href="#reset">reset</a>().
<h3 class=fn>bool <a name="isInvertible"></a>QWMatrix::isInvertible () const
</h3>
<p> Returns TRUE if the matrix is invertible; otherwise returns FALSE.
<p> <p>See also <a href="#invert">invert</a>().
<h3 class=fn>double <a name="m11"></a>QWMatrix::m11 () const
</h3>
<p> Returns the X scaling factor.
<h3 class=fn>double <a name="m12"></a>QWMatrix::m12 () const
</h3>
<p> Returns the vertical shearing factor.
<h3 class=fn>double <a name="m21"></a>QWMatrix::m21 () const
</h3>
<p> Returns the horizontal shearing factor.
<h3 class=fn>double <a name="m22"></a>QWMatrix::m22 () const
</h3>
<p> Returns the Y scaling factor.
<h3 class=fn>void <a name="map"></a>QWMatrix::map ( int x, int y, int * tx, int * ty ) const
</h3>
Transforms ( <em>x</em>, <em>y</em> ) to ( <em>*tx</em>, <em>*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>
<p>Examples: <a href="t14.html#x2247">t14/cannon.cpp</a> and <a href="xform-example.html#x134">xform/xform.cpp</a>.
<h3 class=fn>void <a name="map-2"></a>QWMatrix::map ( double x, double y, double * tx, double * ty ) const
</h3>
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
<p> Transforms ( <em>x</em>, <em>y</em> ) to ( <em>*tx</em>, <em>*ty</em> ) using the following formulae:
<p> <pre>
*tx = m11*x + m21*y + dx
*ty = m22*y + m12*x + dy
</pre>
<h3 class=fn><a href="qpoint.html">QPoint</a> <a name="map-3"></a>QWMatrix::map ( const <a href="qpoint.html">QPoint</a> & p ) const
</h3>
<p> <b>This function is obsolete.</b> It is provided to keep old source working. We strongly advise against using it in new code.
<p> Does the same as operator *( const <a href="qpoint.html">QPoint</a> &)
<h3 class=fn><a href="qrect.html">QRect</a> <a name="map-4"></a>QWMatrix::map ( const <a href="qrect.html">QRect</a> & r ) const
</h3>
<p> <b>This function is obsolete.</b> It is provided to keep old source working. We strongly advise against using it in new code.
<p> Please use <a href="#mapRect">QWMatrix::mapRect</a>() instead.
<p> Note that this method does return the bounding rectangle of the <em>r</em>, when
shearing or rotations are used.
<h3 class=fn><a href="qpointarray.html">QPointArray</a> <a name="map-5"></a>QWMatrix::map ( const <a href="qpointarray.html">QPointArray</a> & a ) const
</h3>
<p> <b>This function is obsolete.</b> It is provided to keep old source working. We strongly advise against using it in new code.
<p> Does the same as operator *( const <a href="qpointarray.html">QPointArray</a> &)
<h3 class=fn><a href="qrect.html">QRect</a> <a name="mapRect"></a>QWMatrix::mapRect ( const <a href="qrect.html">QRect</a> & rect ) const
</h3>
Returns the transformed rectangle <em>rect</em>.
<p> The bounding rectangle is returned if rotation or shearing has been specified.
<p> If you need to know the exact region <em>rect</em> maps to use <a href="#operator*">operator*</a>().
<p> <p>See also <a href="#operator*">operator*</a>().
<h3 class=fn>bool <a name="operator!-eq"></a>QWMatrix::operator!= ( const <a href="qwmatrix.html">QWMatrix</a> & m ) const
</h3>
Returns TRUE if this matrix is not equal to <em>m</em>; otherwise returns FALSE.
<h3 class=fn><a href="qpoint.html">QPoint</a> <a name="operator*"></a>QWMatrix::operator* ( const <a href="qpoint.html">QPoint</a> & p ) const
</h3>
Transforms <em>p</em> to using the formulae:
<p> <pre>
retx = m11*px + m21*py + dx (rounded to the nearest integer)
rety = m22*py + m12*px + dy (rounded to the nearest integer)
</pre>
<h3 class=fn><a href="qregion.html">QRegion</a> <a name="operator*-2"></a>QWMatrix::operator* ( const <a href="qrect.html">QRect</a> & r ) const
</h3>
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
<p> Transforms the rectangle <em>r</em>.
<p> Rotation and shearing a rectangle results in a more general
region, which is returned here.
<p> Calling this method can be rather expensive, if rotations or
shearing are used. If you just need to know the bounding rectangle
of the returned region, use <a href="#mapRect">mapRect</a>() which is a lot
faster than this function.
<p> <p>See also <a href="#mapRect">QWMatrix::mapRect</a>().
<h3 class=fn><a href="qregion.html">QRegion</a> <a name="operator*-3"></a>QWMatrix::operator* ( const <a href="qregion.html">QRegion</a> & r ) const
</h3>
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
<p> Transforms the region <em>r</em>.
<p> Calling this method can be rather expensive, if rotations or
shearing are used.
<h3 class=fn><a href="qpointarray.html">QPointArray</a> <a name="operator*-4"></a>QWMatrix::operator* ( const <a href="qpointarray.html">QPointArray</a> & a ) const
</h3>
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
<p> Returns the point array <em>a</em> transformed by calling map for each point.
<h3 class=fn><a href="qwmatrix.html">QWMatrix</a> & <a name="operator*-eq"></a>QWMatrix::operator*= ( const <a href="qwmatrix.html">QWMatrix</a> & m )
</h3>
Returns the result of multiplying this matrix with matrix <em>m</em>.
<h3 class=fn>bool <a name="operator-eq-eq"></a>QWMatrix::operator== ( const <a href="qwmatrix.html">QWMatrix</a> & m ) const
</h3>
Returns TRUE if this matrix is equal to <em>m</em>; otherwise returns FALSE.
<h3 class=fn>void <a name="reset"></a>QWMatrix::reset ()
</h3>
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.
<p> <p>See also <a href="#isIdentity">isIdentity</a>().
<h3 class=fn><a href="qwmatrix.html">QWMatrix</a> & <a name="rotate"></a>QWMatrix::rotate ( double a )
</h3>
Rotates the coordinate system <em>a</em> degrees counterclockwise.
<p> Returns a reference to the matrix.
<p> <p>See also <a href="#translate">translate</a>(), <a href="#scale">scale</a>() and <a href="#shear">shear</a>().
<p>Examples: <a href="canvas-example.html#x2555">canvas/canvas.cpp</a>, <a href="desktop-example.html#x1759">desktop/desktop.cpp</a>, <a href="drawdemo-example.html#x1660">drawdemo/drawdemo.cpp</a>, <a href="t14.html#x2248">t14/cannon.cpp</a> and <a href="xform-example.html#x135">xform/xform.cpp</a>.
<h3 class=fn><a href="qwmatrix.html">QWMatrix</a> & <a name="scale"></a>QWMatrix::scale ( double sx, double sy )
</h3>
Scales the coordinate system unit by <em>sx</em> horizontally and <em>sy</em>
vertically.
<p> Returns a reference to the matrix.
<p> <p>See also <a href="#translate">translate</a>(), <a href="#shear">shear</a>() and <a href="#rotate">rotate</a>().
<p>Examples: <a href="canvas-example.html#x2556">canvas/canvas.cpp</a>, <a href="fileiconview-example.html#x1589">fileiconview/qfileiconview.cpp</a>, <a href="movies-example.html#x1111">movies/main.cpp</a>, <a href="qmag-example.html#x728">qmag/qmag.cpp</a>, <a href="qtimage-nsplugin-example.html#x2449">qtimage/qtimage.cpp</a>, <a href="showimg-example.html#x457">showimg/showimg.cpp</a> and <a href="xform-example.html#x136">xform/xform.cpp</a>.
<h3 class=fn>void <a name="setMatrix"></a>QWMatrix::setMatrix ( double m11, double m12, double m21, double m22, double dx, double dy )
</h3>
Sets the matrix elements to the specified values, <em>m11</em>, <em>m12</em>, <em>m21</em>,
<em>m22</em>, <em>dx</em> and <em>dy</em>.
<h3 class=fn><a href="qwmatrix.html">QWMatrix</a> & <a name="shear"></a>QWMatrix::shear ( double sh, double sv )
</h3>
Shears the coordinate system by <em>sh</em> horizontally and <em>sv</em> vertically.
<p> Returns a reference to the matrix.
<p> <p>See also <a href="#translate">translate</a>(), <a href="#scale">scale</a>() and <a href="#rotate">rotate</a>().
<p>Examples: <a href="drawdemo-example.html#x1661">drawdemo/drawdemo.cpp</a> and <a href="xform-example.html#x137">xform/xform.cpp</a>.
<h3 class=fn><a href="qwmatrix.html">QWMatrix</a> & <a name="translate"></a>QWMatrix::translate ( double dx, double dy )
</h3>
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> <p>See also <a href="#scale">scale</a>(), <a href="#shear">shear</a>() and <a href="#rotate">rotate</a>().
<p>Examples: <a href="canvas-example.html#x2557">canvas/canvas.cpp</a>, <a href="drawdemo-example.html#x1662">drawdemo/drawdemo.cpp</a>, <a href="t14.html#x2249">t14/cannon.cpp</a> and <a href="xform-example.html#x138">xform/xform.cpp</a>.
<hr><h2>Related Functions</h2>
<h3 class=fn><a href="qwmatrix.html">QWMatrix</a> <a name="operator*-5"></a>operator* ( const <a href="qwmatrix.html">QWMatrix</a> & m1, const <a href="qwmatrix.html">QWMatrix</a> & m2 )
</h3>
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
<p>
Returns the product of <em>m1</em> * <em>m2</em>.
<p> Note that matrix multiplication is not commutative, i.e.
a*b != b*a.
<h3 class=fn><a href="qdatastream.html">QDataStream</a> & <a name="operator-lt-lt"></a>operator<< ( <a href="qdatastream.html">QDataStream</a> & s, const <a href="qwmatrix.html">QWMatrix</a> & m )
</h3>
Writes the matrix <em>m</em> to the stream <em>s</em> and returns a reference to the stream.
<p> <p>See also <a href="datastreamformat.html">Format of the QDataStream operators</a>.
<h3 class=fn><a href="qdatastream.html">QDataStream</a> & <a name="operator-gt-gt"></a>operator>> ( <a href="qdatastream.html">QDataStream</a> & s, <a href="qwmatrix.html">QWMatrix</a> & m )
</h3>
Reads the matrix <em>m</em> from the stream <em>s</em> and returns a reference to the stream.
<p> <p>See also <a href="datastreamformat.html">Format of the QDataStream operators</a>.
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