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<title>The Coordinate System</title>
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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>The Coordinate System</h1>
<p> A <a href="ntqpaintdevice.html">paint device</a> in TQt is a drawable 2D
surface. <a href="tqwidget.html">TQWidget</a>, <a href="ntqpixmap.html">TQPixmap</a>, <a href="ntqpicture.html">TQPicture</a> and <a href="ntqprinter.html">TQPrinter</a> are all
paint devices. A <a href="ntqpainter.html">TQPainter</a> is an object which can draw on such
devices.
<p> The default coordinate system of a paint device has its origin at the
top left corner. X increases to the right and Y increases downwards.
The unit is one pixel on pixel-based devices and one point on
printers.
<p> <h2> An Example
</h2>
<a name="1"></a><p> The illustration below shows a highly magnified portion of the top
left corner of a paint device.
<p> <center><img src="coordsys.png"></center>
<p> The rectangle and the line were drawn by this code (with the grid
added and colors touched up in the illustration):
<p> <pre>
void MyWidget::paintEvent( <a href="qpaintevent.html">TQPaintEvent</a> * )
{
<a href="ntqpainter.html">TQPainter</a> p( this );
p.<a href="ntqpainter.html#setPen">setPen</a>( darkGray );
p.<a href="ntqpainter.html#drawRect">drawRect</a>( 1,2, 5,4 );
p.<a href="ntqpainter.html#setPen">setPen</a>( lightGray );
p.<a href="ntqpainter.html#drawLine">drawLine</a>( 9,2, 7,7 );
}
</pre>
<p> Note that all of the pixels drawn by drawRect() are inside the size
specified (5*4 pixels). This is different from some toolkits; in TQt
the size you specify exactly encompasses the pixels drawn. This
applies to all the relevant functions in <a href="ntqpainter.html">TQPainter</a>.
<p> Similarly, the drawLine() call draws both endpoints of the line, not
just one.
<p> Here are the classes that relate most closely to the coordinate
system:
<p> <center><table cellpadding="4" cellspacing="2" border="0">
<tr bgcolor="#f0f0f0"> <td valign="top"><a href="ntqpoint.html">TQPoint</a>
<td valign="top">A single 2D point in the coordinate system. Most functions in
TQt that deal with points can accept either a <a href="ntqpoint.html">TQPoint</a> argument
or two ints, for example <a href="ntqpainter.html#drawPoint">TQPainter::drawPoint</a>().
<tr bgcolor="#d0d0d0"> <td valign="top"><a href="ntqsize.html">TQSize</a>
<td valign="top">A single 2D vector. Internally, TQPoint and <a href="ntqsize.html">TQSize</a> are the same,
but a point is not the same as a size, so both classes exist.
Again, most functions accept either a TQSize or two ints, for
example <a href="tqwidget.html#resize">TQWidget::resize</a>().
<tr bgcolor="#f0f0f0"> <td valign="top"><a href="ntqrect.html">TQRect</a>
<td valign="top">A 2D rectangle. Most functions accept either a <a href="ntqrect.html">TQRect</a> or four
ints, for example <a href="tqwidget.html#setGeometry">TQWidget::setGeometry</a>().
<tr bgcolor="#d0d0d0"> <td valign="top"><a href="ntqregion.html">TQRegion</a>
<td valign="top">An arbitrary set of points, including all the normal set
operations, e.g. <a href="ntqregion.html#intersect">TQRegion::intersect</a>(), and also a less
usual function to return a list of rectangles whose union is
equal to the region. <a href="ntqregion.html">TQRegion</a> is used e.g. by <a href="ntqpainter.html#setClipRegion">TQPainter::setClipRegion</a>(), <a href="tqwidget.html#repaint">TQWidget::repaint</a>() and <a href="qpaintevent.html#region">TQPaintEvent::region</a>().
<tr bgcolor="#f0f0f0"> <td valign="top"><a href="ntqpainter.html">TQPainter</a>
<td valign="top">The class that paints. It can paint on any device with the
same code. There are differences between devices, <a href="ntqprinter.html#newPage">TQPrinter::newPage</a>() is a good example, but <a href="ntqpainter.html">TQPainter</a> works the
same way on all devices.
<tr bgcolor="#d0d0d0"> <td valign="top"><a href="ntqpaintdevice.html">TQPaintDevice</a>
<td valign="top">A device on which TQPainter can paint. There are two internal
devices, both pixel-based, and two external devices, <a href="ntqprinter.html">TQPrinter</a> and <a href="ntqpicture.html">TQPicture</a> (which records TQPainter commands to a
file or other <a href="ntqiodevice.html">TQIODevice</a>, and plays them back). Other
devices can be defined.
</table></center>
<p> <h2> Transformations
</h2>
<a name="2"></a><p> Although TQt's default coordinate system works as described above, <a href="ntqpainter.html">TQPainter</a> also supports arbitrary transformations.
<p> This transformation engine is a three-step pipeline, closely following
the model outlined in books such as
<a href="http://www.amazon.com/exec/obidos/ASIN/0201848406/trolltech/t">Foley & Van Dam</a> and the
<a href="http://www.amazon.com/exec/obidos/ASIN/0201604582/trolltech/t">OpenGL Programming Guide.</a> Refer to those for in-depth
coverage; here we give just a brief overview and an example.
<p> The first step uses the world <a href="ntqwmatrix.html#TransformationMode">transformation matrix</a>. Use this matrix
to orient and position your objects in your model. TQt provides
methods such as <a href="ntqpainter.html#rotate">TQPainter::rotate</a>(), <a href="ntqpainter.html#scale">TQPainter::scale</a>(), <a href="ntqpainter.html#translate">TQPainter::translate</a>() and so on to operate on this matrix.
<p> <a href="ntqpainter.html#save">TQPainter::save</a>() and <a href="ntqpainter.html#restore">TQPainter::restore</a>() save and restore this
matrix. You can also use <a href="ntqwmatrix.html">TQWMatrix</a> objects, <a href="ntqpainter.html#worldMatrix">TQPainter::worldMatrix</a>() and <a href="ntqpainter.html#setWorldMatrix">TQPainter::setWorldMatrix</a>() to store and
use named matrices.
<p> The second step uses the window. The window describes the view
boundaries in model coordinates. The matrix positions the <em>objects</em>
and <a href="ntqpainter.html#setWindow">TQPainter::setWindow</a>() positions the <em>window</em>, deciding what
coordinates will be visible. (If you have 3D experience, the window
is what's usually called projection in 3D.)
<p> The third step uses the viewport. The viewport too, describes the view
boundaries, but in device coordinates. The viewport and the windows
describe the same rectangle, but in different coordinate systems.
<p> On-screen, the default is the entire <a href="tqwidget.html">TQWidget</a> or <a href="ntqpixmap.html">TQPixmap</a> where
you are drawing, which is usually appropriate. For printing this
function is vital, since very few printers can print over the entire
physical page.
<p> So each object to be drawn is transformed into model
coordinates using <a href="ntqpainter.html#worldMatrix">TQPainter::worldMatrix</a>(), then positioned
on the drawing device using <a href="ntqpainter.html#window">TQPainter::window</a>() and
<a href="ntqpainter.html#viewport">TQPainter::viewport</a>().
<p> It is perfectly possible to do without one or two of the stages. If,
for example, your goal is to draw something scaled, then just using <a href="ntqpainter.html#scale">TQPainter::scale</a>() makes perfect sense. If your goal is to use a
fixed-size coordinate system, <a href="ntqpainter.html#setWindow">TQPainter::setWindow</a>() is
ideal. And so on.
<p> Here is a short example that uses all three mechanisms: the function
that draws the clock face in the <a href="aclock-example.html">aclock/aclock.cpp</a> example. We
recommend compiling and running the example before you read any
further. In particular, try resizing the window to different sizes.
<p>
<pre> void AnalogClock::drawClock( <a href="ntqpainter.html">TQPainter</a> *paint )
{
<a name="x2275"></a> paint-><a href="ntqpainter.html#save">save</a>();
</pre>
<p> Firstly, we save the painter's state, so that the calling function
is guaranteed not to be disturbed by the transformations we're going
to use.
<p> <pre> <a name="x2277"></a> paint-><a href="ntqpainter.html#setWindow">setWindow</a>( -500,-500, 1000,1000 );
</pre>
<p> We set the model coordinate system we want a 1000*1000 window where
0,0 is in the middle.
<p> <pre> <a name="x2278"></a> <a href="ntqrect.html">TQRect</a> v = paint-><a href="ntqpainter.html#viewport">viewport</a>();
<a name="x2282"></a><a name="x2279"></a> int d = TQMIN( v.<a href="ntqrect.html#width">width</a>(), v.<a href="ntqrect.html#height">height</a>() );
</pre>
<p> The device may not be square and we want the clock to be, so we find
its current viewport and compute its shortest side.
<p> <pre> <a name="x2280"></a><a name="x2276"></a> paint-><a href="ntqpainter.html#setViewport">setViewport</a>( v.<a href="ntqrect.html#left">left</a>() + (v.<a href="ntqrect.html#width">width</a>()-d)/2,
<a name="x2281"></a> v.<a href="ntqrect.html#top">top</a>() + (v.<a href="ntqrect.html#height">height</a>()-d)/2, d, d );
</pre>
<p> Then we set a new square viewport, centered in the old one.
<p> We're now done with our view. From this point on, when we draw in a
1000*1000 area around 0,0, what we draw will show up in the largest
possible square that'll fit in the output device.
<p> Time to start drawing.
<p> <pre> <a href="ntqpointarray.html">TQPointArray</a> pts;
</pre>
<p> <em>pts</em> is just a temporary variable to hold some points.
<p> Next come three drawing blocks, one for the hour hand, one for the
minute hand and finally one for the clock face itself. First we draw
the hour hand:
<p> <pre> paint-><a href="ntqpainter.html#save">save</a>();
<a name="x2274"></a> paint-><a href="ntqpainter.html#rotate">rotate</a>( 30*(time.hour()%12-3) + time.minute()/2 );
</pre>
<p> We save the painter and then rotate it so that one axis points along
the hour hand.
<p> <pre> pts.setPoints( 4, -20,0, 0,-20, 300,0, 0,20 );
<a name="x2271"></a> paint-><a href="ntqpainter.html#drawConvexPolygon">drawConvexPolygon</a>( pts );
</pre>
<p> We set <em>pts</em> to a four-point polygon that looks like the hour hand at
three o'clock, and draw it. Because of the rotation, it's drawn
pointed in the right direction.
<p> <pre> <a name="x2273"></a> paint-><a href="ntqpainter.html#restore">restore</a>();
</pre>
<p> We restore the saved painter, undoing the rotation. We could also
call rotate( -30 ) but that might introduce rounding errors, so it's
better to use save() and restore(). Next, the minute hand, drawn
almost the same way:
<p> <pre> paint-><a href="ntqpainter.html#save">save</a>();
paint-><a href="ntqpainter.html#rotate">rotate</a>( (time.minute()-15)*6 );
pts.setPoints( 4, -10,0, 0,-10, 400,0, 0,10 );
paint-><a href="ntqpainter.html#drawConvexPolygon">drawConvexPolygon</a>( pts );
paint-><a href="ntqpainter.html#restore">restore</a>();
</pre>
<p> The only differences are how the rotation angle is computed and the
shape of the polygon.
<p> The last part to be drawn is the clock face itself.
<p> <pre> for ( int i=0; i<12; i++ ) {
<a name="x2272"></a> paint-><a href="ntqpainter.html#drawLine">drawLine</a>( 440,0, 460,0 );
paint-><a href="ntqpainter.html#rotate">rotate</a>( 30 );
}
</pre>
<p> Twelve short hour lines at thirty-degree intervals. At the end of
that, the painter is rotated in a way which isn't very useful, but
we're done with painting so that doesn't matter.
<p> <pre> paint-><a href="ntqpainter.html#restore">restore</a>();
}
</pre>
<p> The final line of the function restores the painter, so that the
caller won't be affected by all the transformations we've done.
<p>
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