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6<title>The Coordinate System</title>
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32<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>
33
34
35
36<p> A <a href="qpaintdevice.html">paint device</a> in Qt is a drawable 2D
37surface. <a href="qwidget.html">QWidget</a>, <a href="qpixmap.html">QPixmap</a>, <a href="qpicture.html">QPicture</a> and <a href="qprinter.html">QPrinter</a> are all
38paint devices. A <a href="qpainter.html">QPainter</a> is an object which can draw on such
39devices.
40<p> The default coordinate system of a paint device has its origin at the
41top left corner. X increases to the right and Y increases downwards.
42The unit is one pixel on pixel-based devices and one point on
43printers.
44<p> <h2> An Example
45</h2>
46<a name="1"></a><p> The illustration below shows a highly magnified portion of the top
47left corner of a paint device.
48<p> <center><img src="coordsys.png"></center>
49<p> The rectangle and the line were drawn by this code (with the grid
50added and colors touched up in the illustration):
51<p> <pre>
52 void MyWidget::paintEvent( <a href="qpaintevent.html">QPaintEvent</a> * )
53 {
54 <a href="qpainter.html">QPainter</a> p( this );
55 p.<a href="qpainter.html#setPen">setPen</a>( darkGray );
56 p.<a href="qpainter.html#drawRect">drawRect</a>( 1,2, 5,4 );
57 p.<a href="qpainter.html#setPen">setPen</a>( lightGray );
58 p.<a href="qpainter.html#drawLine">drawLine</a>( 9,2, 7,7 );
59 }
60</pre>
61
62<p> Note that all of the pixels drawn by drawRect() are inside the size
63specified (5*4 pixels). This is different from some toolkits; in Qt
64the size you specify exactly encompasses the pixels drawn. This
65applies to all the relevant functions in <a href="qpainter.html">QPainter</a>.
66<p> Similarly, the drawLine() call draws both endpoints of the line, not
67just one.
68<p> Here are the classes that relate most closely to the coordinate
69system:
70<p> <center><table cellpadding="4" cellspacing="2" border="0">
71<tr bgcolor="#f0f0f0"> <td valign="top"><a href="qpoint.html">QPoint</a>
72<td valign="top">A single 2D point in the coordinate system. Most functions in
73Qt that deal with points can accept either a <a href="qpoint.html">QPoint</a> argument
74or two ints, for example <a href="qpainter.html#drawPoint">QPainter::drawPoint</a>().
75<tr bgcolor="#d0d0d0"> <td valign="top"><a href="qsize.html">QSize</a>
76<td valign="top">A single 2D vector. Internally, QPoint and <a href="qsize.html">QSize</a> are the same,
77but a point is not the same as a size, so both classes exist.
78Again, most functions accept either a QSize or two ints, for
79example <a href="qwidget.html#resize">QWidget::resize</a>().
80<tr bgcolor="#f0f0f0"> <td valign="top"><a href="qrect.html">QRect</a>
81<td valign="top">A 2D rectangle. Most functions accept either a <a href="qrect.html">QRect</a> or four
82ints, for example <a href="qwidget.html#setGeometry">QWidget::setGeometry</a>().
83<tr bgcolor="#d0d0d0"> <td valign="top"><a href="qregion.html">QRegion</a>
84<td valign="top">An arbitrary set of points, including all the normal set
85operations, e.g. <a href="qregion.html#intersect">QRegion::intersect</a>(), and also a less
86usual function to return a list of rectangles whose union is
87equal to the region. <a href="qregion.html">QRegion</a> is used e.g. by <a href="qpainter.html#setClipRegion">QPainter::setClipRegion</a>(), <a href="qwidget.html#repaint">QWidget::repaint</a>() and <a href="qpaintevent.html#region">QPaintEvent::region</a>().
88<tr bgcolor="#f0f0f0"> <td valign="top"><a href="qpainter.html">QPainter</a>
89<td valign="top">The class that paints. It can paint on any device with the
90same code. There are differences between devices, <a href="qprinter.html#newPage">QPrinter::newPage</a>() is a good example, but <a href="qpainter.html">QPainter</a> works the
91same way on all devices.
92<tr bgcolor="#d0d0d0"> <td valign="top"><a href="qpaintdevice.html">QPaintDevice</a>
93<td valign="top">A device on which QPainter can paint. There are two internal
94devices, both pixel-based, and two external devices, <a href="qprinter.html">QPrinter</a> and <a href="qpicture.html">QPicture</a> (which records QPainter commands to a
95file or other <a href="qiodevice.html">QIODevice</a>, and plays them back). Other
96devices can be defined.
97</table></center>
98<p> <h2> Transformations
99</h2>
100<a name="2"></a><p> Although Qt's default coordinate system works as described above, <a href="qpainter.html">QPainter</a> also supports arbitrary transformations.
101<p> This transformation engine is a three-step pipeline, closely following
102the model outlined in books such as
103<a href="http://www.amazon.com/exec/obidos/ASIN/0201848406/trolltech/t">Foley &amp; Van Dam</a> and the
104<a href="http://www.amazon.com/exec/obidos/ASIN/0201604582/trolltech/t">OpenGL Programming Guide.</a> Refer to those for in-depth
105coverage; here we give just a brief overview and an example.
106<p> The first step uses the world <a href="qwmatrix.html#TransformationMode">transformation matrix</a>. Use this matrix
107to orient and position your objects in your model. Qt provides
108methods such as <a href="qpainter.html#rotate">QPainter::rotate</a>(), <a href="qpainter.html#scale">QPainter::scale</a>(), <a href="qpainter.html#translate">QPainter::translate</a>() and so on to operate on this matrix.
109<p> <a href="qpainter.html#save">QPainter::save</a>() and <a href="qpainter.html#restore">QPainter::restore</a>() save and restore this
110matrix. You can also use <a href="qwmatrix.html">QWMatrix</a> objects, <a href="qpainter.html#worldMatrix">QPainter::worldMatrix</a>() and <a href="qpainter.html#setWorldMatrix">QPainter::setWorldMatrix</a>() to store and
111use named matrices.
112<p> The second step uses the window. The window describes the view
113boundaries in model coordinates. The matrix positions the <em>objects</em>
114and <a href="qpainter.html#setWindow">QPainter::setWindow</a>() positions the <em>window</em>, deciding what
115coordinates will be visible. (If you have 3D experience, the window
116is what's usually called projection in 3D.)
117<p> The third step uses the viewport. The viewport too, describes the view
118boundaries, but in device coordinates. The viewport and the windows
119describe the same rectangle, but in different coordinate systems.
120<p> On-screen, the default is the entire <a href="qwidget.html">QWidget</a> or <a href="qpixmap.html">QPixmap</a> where
121you are drawing, which is usually appropriate. For printing this
122function is vital, since very few printers can print over the entire
123physical page.
124<p> So each object to be drawn is transformed into model
125coordinates using <a href="qpainter.html#worldMatrix">QPainter::worldMatrix</a>(), then positioned
126on the drawing device using <a href="qpainter.html#window">QPainter::window</a>() and
127<a href="qpainter.html#viewport">QPainter::viewport</a>().
128<p> It is perfectly possible to do without one or two of the stages. If,
129for example, your goal is to draw something scaled, then just using <a href="qpainter.html#scale">QPainter::scale</a>() makes perfect sense. If your goal is to use a
130fixed-size coordinate system, <a href="qpainter.html#setWindow">QPainter::setWindow</a>() is
131ideal. And so on.
132<p> Here is a short example that uses all three mechanisms: the function
133that draws the clock face in the <a href="aclock-example.html">aclock/aclock.cpp</a> example. We
134recommend compiling and running the example before you read any
135further. In particular, try resizing the window to different sizes.
136<p>
137
138<pre> void AnalogClock::drawClock( <a href="qpainter.html">QPainter</a> *paint )
139 {
140 <a name="x2275"></a> paint-&gt;<a href="qpainter.html#save">save</a>();
141</pre>
142<p> Firstly, we save the painter's state, so that the calling function
143is guaranteed not to be disturbed by the transformations we're going
144to use.
145<p> <pre> <a name="x2277"></a> paint-&gt;<a href="qpainter.html#setWindow">setWindow</a>( -500,-500, 1000,1000 );
146</pre>
147<p> We set the model coordinate system we want a 1000*1000 window where
1480,0 is in the middle.
149<p> <pre> <a name="x2278"></a> <a href="qrect.html">QRect</a> v = paint-&gt;<a href="qpainter.html#viewport">viewport</a>();
150 <a name="x2282"></a><a name="x2279"></a> int d = QMIN( v.<a href="qrect.html#width">width</a>(), v.<a href="qrect.html#height">height</a>() );
151</pre>
152<p> The device may not be square and we want the clock to be, so we find
153its current viewport and compute its shortest side.
154<p> <pre> <a name="x2280"></a><a name="x2276"></a> paint-&gt;<a href="qpainter.html#setViewport">setViewport</a>( v.<a href="qrect.html#left">left</a>() + (v.<a href="qrect.html#width">width</a>()-d)/2,
155 <a name="x2281"></a> v.<a href="qrect.html#top">top</a>() + (v.<a href="qrect.html#height">height</a>()-d)/2, d, d );
156</pre>
157<p> Then we set a new square viewport, centered in the old one.
158<p> We're now done with our view. From this point on, when we draw in a
1591000*1000 area around 0,0, what we draw will show up in the largest
160possible square that'll fit in the output device.
161<p> Time to start drawing.
162<p> <pre> <a href="qpointarray.html">QPointArray</a> pts;
163</pre>
164<p> <em>pts</em> is just a temporary variable to hold some points.
165<p> Next come three drawing blocks, one for the hour hand, one for the
166minute hand and finally one for the clock face itself. First we draw
167the hour hand:
168<p> <pre> paint-&gt;<a href="qpainter.html#save">save</a>();
169 <a name="x2274"></a> paint-&gt;<a href="qpainter.html#rotate">rotate</a>( 30*(time.hour()%12-3) + time.minute()/2 );
170</pre>
171<p> We save the painter and then rotate it so that one axis points along
172the hour hand.
173<p> <pre> pts.setPoints( 4, -20,0, 0,-20, 300,0, 0,20 );
174 <a name="x2271"></a> paint-&gt;<a href="qpainter.html#drawConvexPolygon">drawConvexPolygon</a>( pts );
175</pre>
176<p> We set <em>pts</em> to a four-point polygon that looks like the hour hand at
177three o'clock, and draw it. Because of the rotation, it's drawn
178pointed in the right direction.
179<p> <pre> <a name="x2273"></a> paint-&gt;<a href="qpainter.html#restore">restore</a>();
180</pre>
181<p> We restore the saved painter, undoing the rotation. We could also
182call rotate( -30 ) but that might introduce rounding errors, so it's
183better to use save() and restore(). Next, the minute hand, drawn
184almost the same way:
185<p> <pre> paint-&gt;<a href="qpainter.html#save">save</a>();
186 paint-&gt;<a href="qpainter.html#rotate">rotate</a>( (time.minute()-15)*6 );
187 pts.setPoints( 4, -10,0, 0,-10, 400,0, 0,10 );
188 paint-&gt;<a href="qpainter.html#drawConvexPolygon">drawConvexPolygon</a>( pts );
189 paint-&gt;<a href="qpainter.html#restore">restore</a>();
190</pre>
191<p> The only differences are how the rotation angle is computed and the
192shape of the polygon.
193<p> The last part to be drawn is the clock face itself.
194<p> <pre> for ( int i=0; i&lt;12; i++ ) {
195 <a name="x2272"></a> paint-&gt;<a href="qpainter.html#drawLine">drawLine</a>( 440,0, 460,0 );
196 paint-&gt;<a href="qpainter.html#rotate">rotate</a>( 30 );
197 }
198</pre>
199<p> Twelve short hour lines at thirty-degree intervals. At the end of
200that, the painter is rotated in a way which isn't very useful, but
201we're done with painting so that doesn't matter.
202<p> <pre> paint-&gt;<a href="qpainter.html#restore">restore</a>();
203 }
204</pre>
205<p> The final line of the function restores the painter, so that the
206caller won't be affected by all the transformations we've done.
207<p>
208<!-- eof -->
209<p><address><hr><div align=center>
210<table width=100% cellspacing=0 border=0><tr>
211<td>Copyright &copy; 2007
212<a href="troll.html">Trolltech</a><td align=center><a href="trademarks.html">Trademarks</a>
213<td align=right><div align=right>Qt 3.3.8</div>
214</table></div></address></body>
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