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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 class=fn><a href="#QWMatrix"><b>QWMatrix</b></a> ()</li>
<li class=fn><a href="#QWMatrix-2"><b>QWMatrix</b></a> ( double m11, double m12, double m21, double m22, double dx, double dy )</li>
<li class=fn>void <a href="#setMatrix"><b>setMatrix</b></a> ( double m11, double m12, double m21, double m22, double dx, double dy )</li>
<li class=fn>double <a href="#m11"><b>m11</b></a> () const</li>
<li class=fn>double <a href="#m12"><b>m12</b></a> () const</li>
<li class=fn>double <a href="#m21"><b>m21</b></a> () const</li>
<li class=fn>double <a href="#m22"><b>m22</b></a> () const</li>
<li class=fn>double <a href="#dx"><b>dx</b></a> () const</li>
<li class=fn>double <a href="#dy"><b>dy</b></a> () const</li>
<li class=fn>void <a href="#map"><b>map</b></a> ( int x, int y, int * tx, int * ty ) const</li>
<li class=fn>void <a href="#map-2"><b>map</b></a> ( double x, double y, double * tx, double * ty ) const</li>
<li class=fn>QRect <a href="#mapRect"><b>mapRect</b></a> ( const QRect & rect ) const</li>
<li class=fn>QPoint <a href="#map-3"><b>map</b></a> ( const QPoint & p ) const</li>
<li class=fn>QRect map ( const QRect & r ) const <em>(obsolete)</em></li>
<li class=fn>QPointArray <a href="#map-5"><b>map</b></a> ( const QPointArray & a ) const</li>
<li class=fn>QRegion <a href="#map-6"><b>map</b></a> ( const QRegion & r ) const</li>
<li class=fn>QRegion <a href="#mapToRegion"><b>mapToRegion</b></a> ( const QRect & rect ) const</li>
<li class=fn>QPointArray <a href="#mapToPolygon"><b>mapToPolygon</b></a> ( const QRect & rect ) const</li>
<li class=fn>void <a href="#reset"><b>reset</b></a> ()</li>
<li class=fn>bool <a href="#isIdentity"><b>isIdentity</b></a> () const</li>
<li class=fn>QWMatrix & <a href="#translate"><b>translate</b></a> ( double dx, double dy )</li>
<li class=fn>QWMatrix & <a href="#scale"><b>scale</b></a> ( double sx, double sy )</li>
<li class=fn>QWMatrix & <a href="#shear"><b>shear</b></a> ( double sh, double sv )</li>
<li class=fn>QWMatrix & <a href="#rotate"><b>rotate</b></a> ( double a )</li>
<li class=fn>bool <a href="#isInvertible"><b>isInvertible</b></a> () const</li>
<li class=fn>double <a href="#det"><b>det</b></a> () const</li>
<li class=fn>QWMatrix <a href="#invert"><b>invert</b></a> ( bool * invertible = 0 ) const</li>
<li class=fn>bool <a href="#operator-eq-eq"><b>operator==</b></a> ( const QWMatrix & m ) const</li>
<li class=fn>bool <a href="#operator!-eq"><b>operator!=</b></a> ( const QWMatrix & m ) const</li>
<li class=fn>QWMatrix & <a href="#operator*-eq"><b>operator*=</b></a> ( const QWMatrix & m )</li>
<li class=fn>enum <a href="#TransformationMode-enum"><b>TransformationMode</b></a> { Points, Areas }</li>
</ul>
<h2>Static Public Members</h2>
<ul>
<li class=fn>void <a href="#setTransformationMode"><b>setTransformationMode</b></a> ( QWMatrix::TransformationMode m )</li>
<li class=fn>TransformationMode <a href="#transformationMode"><b>transformationMode</b></a> ()</li>
</ul>
<h2>Related Functions</h2>
<ul>
<li class=fn>QDataStream & <a href="#operator-lt-lt"><b>operator<<</b></a> ( QDataStream & s, const QWMatrix & m )</li>
<li class=fn>QDataStream & <a href="#operator-gt-gt"><b>operator>></b></a> ( QDataStream & s, QWMatrix & m )</li>
</ul>
<hr><a name="details"></a><h2>Detailed Description</h2>
The QWMatrix class specifies 2D transformations of a
coordinate system.
<p>
<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 the 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 3x3 matrix of the form:
<table align=center border=1 cellpadding=1 cellspacing=0>
<tr align=center><td>m11</td><td>m12</td><td> 0 </td></tr>
<tr align=center><td>m21</td><td>m22</td><td> 0 </td></tr>
<tr align=center><td>dx</td> <td>dy</td> <td> 1 </td></tr>
</table>
<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 also 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(1, 0, 0, 1, 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 Type Documentation</h2>
<h3 class=fn><a name="TransformationMode-enum"></a>QWMatrix::TransformationMode</h3>
<p> <!-- index transformation matrix -->
<p> QWMatrix offers two transformation modes. Calculations can either
be done in terms of points (Points mode, the default), or in
terms of area (Area mode).
<p> In Points mode the transformation is applied to the points that
mark out the shape's bounding line. In Areas mode the
transformation is applied in such a way that the area of the
contained region is correctly transformed under the matrix.
<ul>
<li><tt>QWMatrix::Points</tt> - transformations are applied to the shape's points.
<li><tt>QWMatrix::Areas</tt> - transformations are applied (e.g. to the width and
height) so that the area is transformed.
</ul><p> Example:
<p> Suppose we have a rectangle,
<tt>QRect( 10, 20, 30, 40 )</tt> and a transformation matrix
<tt>QWMatrix( 2, 0, 0, 2, 0, 0 )</tt> to double the rectangle's size.
<p> In Points mode, the matrix will transform the top-left (10,20) and
the bottom-right (39,59) points producing a rectangle with its
top-left point at (20,40) and its bottom-right point at (78,118),
i.e. with a width of 59 and a height of 79.
<p> In Areas mode, the matrix will transform the top-left point in
the same way as in Points mode to (20/40), and double the width
and height, so the bottom-right will become (69,99), i.e. a width
of 60 and a height of 80.
<p> Because integer arithmetic is used (for speed), rounding
differences mean that the modes will produce slightly different
results given the same shape and the same transformation,
especially when scaling up. This also means that some operations
are not commutative.
<p> Under Points mode, <tt>matrix * ( region1 | region2 )</tt> is not equal to
<tt>matrix * region1 | matrix * region2</tt>. Under Area mode, <tt>matrix * (pointarray[i])</tt> is not neccesarily equal to
<tt>(matrix * pointarry)[i]</tt>.
<p> <center><img src="xform.png" alt="Comparison of Points and Areas TransformationModes"></center>
<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="det"></a>QWMatrix::det () const
</h3>
<p> Returns the matrix's determinant.
<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 0: the value of <em>*invertible</em> is set
to TRUE if the matrix is invertible; otherwise <em>*invertible</em> is
set to FALSE.
<p> <p>See also <a href="#isInvertible">isInvertible</a>().
<p>Example: <a href="tutorial1-14.html#x2433">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="tutorial1-14.html#x2434">t14/cannon.cpp</a> and <a href="xform-example.html#x1278">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> This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
<p> 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="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> 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="qregion.html">QRegion</a> <a name="map-6"></a>QWMatrix::map ( const <a href="qregion.html">QRegion</a> & r ) const
</h3>
<p> 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="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="qsize.html#operator*-4">operator*</a>().
<p> <p>See also <a href="qsize.html#operator*-4">operator*</a>().
<p>Example: <a href="xform-example.html#x1279">xform/xform.cpp</a>.
<h3 class=fn><a href="qpointarray.html">QPointArray</a> <a name="mapToPolygon"></a>QWMatrix::mapToPolygon ( const <a href="qrect.html">QRect</a> & rect ) const
</h3>
Returns the transformed rectangle <em>rect</em> as a polygon.
<p> Polygons and rectangles behave slightly differently
when transformed (due to integer rounding), so
<tt>matrix.map( QPointArray( rect ) )</tt> is not always the same as
<tt>matrix.mapToPolygon( rect )</tt>.
<h3 class=fn><a href="qregion.html">QRegion</a> <a name="mapToRegion"></a>QWMatrix::mapToRegion ( const <a href="qrect.html">QRect</a> & rect ) const
</h3>
<p> Returns the transformed rectangle <em>rect</em>.
<p> A rectangle which has been rotated or sheared may result in a
non-rectangular region being returned.
<p> Calling this method can be 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>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="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 by 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)
which 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#x2955">canvas/canvas.cpp</a>, <a href="desktop-example.html#x1764">desktop/desktop.cpp</a>, <a href="drawdemo-example.html#x1095">drawdemo/drawdemo.cpp</a>, <a href="tutorial1-14.html#x2435">t14/cannon.cpp</a>, and <a href="xform-example.html#x1280">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#x2956">canvas/canvas.cpp</a>, <a href="fileiconview-example.html#x876">fileiconview/qfileiconview.cpp</a>, <a href="movies-example.html#x524">movies/main.cpp</a>, <a href="qmag-example.html#x1809">qmag/qmag.cpp</a>, <a href="showimg-example.html#x1357">showimg/showimg.cpp</a>, and <a href="xform-example.html#x1281">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>void <a name="setTransformationMode"></a>QWMatrix::setTransformationMode ( <a href="qwmatrix.html#TransformationMode-enum">QWMatrix::TransformationMode</a> m )<tt> [static]</tt>
</h3>
Sets the transformation mode that QWMatrix and painter
transformations use to <em>m</em>.
<p> <p>See also <a href="#TransformationMode-enum">QWMatrix::TransformationMode</a>.
<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#x1096">drawdemo/drawdemo.cpp</a> and <a href="xform-example.html#x1282">xform/xform.cpp</a>.
<h3 class=fn><a href="qwmatrix.html#TransformationMode-enum">TransformationMode</a> <a name="transformationMode"></a>QWMatrix::transformationMode ()<tt> [static]</tt>
</h3>
Returns the current transformation mode.
<p> <p>See also <a href="#TransformationMode-enum">QWMatrix::TransformationMode</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#x2957">canvas/canvas.cpp</a>, <a href="drawdemo-example.html#x1097">drawdemo/drawdemo.cpp</a>, <a href="tutorial1-14.html#x2436">t14/cannon.cpp</a>, and <a href="xform-example.html#x1283">xform/xform.cpp</a>.
<hr><h2>Related Functions</h2>
<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>
<p> 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>
<p> 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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