The Coordinate System

Window-Viewport Conversion

When drawing with QPainter, we specify points using logical coordinates which then are converted into the physical coordinates of the paint device.

The mapping of the logical coordinates to the physical coordinates are handled by QPainter's world transformation worldMatrix() (described in the Transformations section), and QPainter's viewport() and window(). The viewport represents the physical coordinates specifying an arbitrary rectangle. The "window" describes the same rectangle in logical coordinates. By default the logical and physical coordinate systems coincide, and are equivalent to the paint device's rectangle.

Using window-viewport conversion you can make the logical coordinate system fit your preferences. The mechanism can also be used to make the drawing code independent of the paint device. You can, for example, make the logical coordinates extend from (-50, -50) to (50, 50) with (0, 0) in the center by calling the QPainter::setWindow() function:

     QPainter painter(this);
     painter.setWindow(QRect(-50, -50, 100, 100));

Now, the logical coordinates (-50,-50) correspond to the paint device's physical coordinates (0, 0). Independent of the paint device, your painting code will always operate on the specified logical coordinates.

By setting the "window" or viewport rectangle, you perform a linear transformation of the coordinates. Note that each corner of the "window" maps to the corresponding corner of the viewport, and vice versa. For that reason it normally is a good idea to let the viewport and "window" maintain the same aspect ratio to prevent deformation:

     int side = qMin(width(), height())
     int x = (width() - side / 2);
     int y = (height() - side / 2);

     painter.setViewport(x, y, side, side);

If we make the logical coordinate system a square, we should also make the viewport a square using the QPainter::setViewport() function. In the example above we make it equivalent to the largest square that fit into the paint device's rectangle. By taking the paint device's size into consideration when setting the window or viewport, it is possible to keep the drawing code independent of the paint device.

Note that the window-viewport conversion is only a linear transformation, i.e. it does not perform clipping. This means that if you paint outside the currently set "window", your painting is still transformed to the viewport using the same linear algebraic approach.

The viewport, "window" and transformation matrix determine how logical QPainter coordinates map to the paint device's physical coordinates. By default the world transformation matrix is the identity matrix, and the "window" and viewport settings are equivalent to the paint device's settings, i.e. the world, "window" and device coordinate systems are equivalent, but as we have seen, the systems can be manipulated using transformation operations and window-viewport conversion. The illustration above describes the process.

See also Analog Clock Example and Transformations Example.