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/*!
    \page coordsys.html
    \title The Coordinate System
    \brief Information about the coordinate system used by the paint
    system.

    \previouspage Drawing and Filling
    \contentspage The Paint System
    \nextpage Reading and Writing Image Files

    The coordinate system is controlled by the QPainter
    class. Together with the QPaintDevice and QPaintEngine classes,
    QPainter form the basis of Qt's painting system, Arthur. QPainter
    is used to perform drawing operations, QPaintDevice is an
    abstraction of a two-dimensional space that can be painted on
    using a QPainter, and QPaintEngine provides the interface that the
    painter uses to draw onto different types of devices.

    The QPaintDevice class is the base class of objects that can be
    painted: Its drawing capabilities are inherited by the QWidget,
    QPixmap, QPicture, QImage, and QPrinter classes. The default
    coordinate system of a paint device has its origin at the top-left
    corner. The \e x values increase to the right and the \e y values
    increase downwards. The default unit is one pixel on pixel-based
    devices and one point (1/72 of an inch) on printers.

    The mapping of the logical QPainter coordinates to the physical
    QPaintDevice coordinates are handled by QPainter's transformation
    matrix, viewport and "window". The logical and physical coordinate
    systems coincide by default. QPainter also supports coordinate
    transformations (e.g. rotation and scaling).

    \tableofcontents

    \section1 Rendering

    \section2 Logical Representation

    The size (width and height) of a graphics primitive always
    correspond to its mathematical model, ignoring the width of the
    pen it is rendered with:

    \table
    \row
    \o \inlineimage coordinatesystem-rect.png
    \o \inlineimage coordinatesystem-line.png
    \row
    \o QRect(1, 2, 6, 4)
    \o QLine(2, 7, 6, 1)
    \endtable

    \section2 Aliased Painting

    When drawing, the pixel rendering is controlled by the
    QPainter::Antialiasing render hint.

    The \l {QPainter::RenderHint}{RenderHint} enum is used to specify
    flags to QPainter that may or may not be respected by any given
    engine. The QPainter::Antialiasing value indicates that the engine
    should antialias edges of primitives if possible, i.e. smoothing
    the edges by using different color intensities.

    But by default the painter is \e aliased and other rules apply:
    When rendering with a one pixel wide pen the pixels will be
    rendered to the \e {right and below the mathematically defined
    points}. For example:

    \table
    \row
    \o \inlineimage coordinatesystem-rect-raster.png
    \o \inlineimage coordinatesystem-line-raster.png

    \row
    \o
    \snippet doc/src/snippets/code/doc_src_coordsys.qdoc 0

    \o
    \snippet doc/src/snippets/code/doc_src_coordsys.qdoc 1
    \endtable

    When rendering with a pen with an even number of pixels, the
    pixels will be rendered symetrically around the mathematical
    defined points, while rendering with a pen with an odd number of
    pixels, the spare pixel will be rendered to the right and below
    the mathematical point as in the one pixel case. See the QRectF
    diagrams below for concrete examples.

    \table
    \header
    \o {3,1} QRectF
    \row
    \o \inlineimage qrect-diagram-zero.png
    \o \inlineimage qrectf-diagram-one.png
    \row
    \o Logical representation
    \o One pixel wide pen
    \row
    \o \inlineimage qrectf-diagram-two.png
    \o \inlineimage qrectf-diagram-three.png
    \row
    \o Two pixel wide pen
    \o Three pixel wide pen
    \endtable

    Note that for historical reasons the return value of the
    QRect::right() and QRect::bottom() functions deviate from the true
    bottom-right corner of the rectangle.

    QRect's \l {QRect::right()}{right()} function returns \l
    {QRect::left()}{left()} + \l {QRect::width()}{width()} - 1 and the
    \l {QRect::bottom()}{bottom()} function returns \l
    {QRect::top()}{top()} + \l {QRect::height()}{height()} - 1.  The
    bottom-right green point in the diagrams shows the return
    coordinates of these functions.

    We recommend that you simply use QRectF instead: The QRectF class
    defines a rectangle in the plane using floating point coordinates
    for accuracy (QRect uses integer coordinates), and the
    QRectF::right() and QRectF::bottom() functions \e do return the
    true bottom-right corner.

    Alternatively, using QRect, apply \l {QRect::x()}{x()} + \l
    {QRect::width()}{width()} and \l {QRect::y()}{y()} + \l
    {QRect::height()}{height()} to find the bottom-right corner, and
    avoid the \l {QRect::right()}{right()} and \l
    {QRect::bottom()}{bottom()} functions.

    \section2 Anti-aliased Painting

    If you set QPainter's \l {QPainter::Antialiasing}{anti-aliasing}
    render hint, the pixels will be rendered symetrically on both
    sides of the mathematically defined points:

    \table
    \row
    \o \inlineimage coordinatesystem-rect-antialias.png
    \o \inlineimage coordinatesystem-line-antialias.png
    \row
    \o

    \snippet doc/src/snippets/code/doc_src_coordsys.qdoc 2

    \o
    \snippet doc/src/snippets/code/doc_src_coordsys.qdoc 3
    \endtable

    \section1 Transformations

    By default, the QPainter operates on the associated device's own
    coordinate system, but it also has complete support for affine
    coordinate transformations.

    You can scale the coordinate system by a given offset using the
    QPainter::scale() function, you can rotate it clockwise using the
    QPainter::rotate() function and you can translate it (i.e. adding
    a given offset to the points) using the QPainter::translate()
    function.

    \table
    \row
    \o \inlineimage qpainter-clock.png
    \o \inlineimage qpainter-rotation.png
    \o \inlineimage qpainter-scale.png
    \o \inlineimage qpainter-translation.png
    \row
    \o nop
    \o \l {QPainter::rotate()}{rotate()}
    \o \l {QPainter::scale()}{scale()}
    \o \l {QPainter::translate()}{translate()}
    \endtable

    You can also twist the coordinate system around the origin using
    the QPainter::shear() function. See the \l {demos/affine}{Affine
    Transformations} demo for a visualization of a sheared coordinate
    system. All the transformation operations operate on QPainter's
    transformation matrix that you can retrieve using the
    QPainter::worldTransform() function. A matrix transforms a point
    in the plane to another point.

    If you need the same transformations over and over, you can also
    use QTransform objects and the QPainter::worldTransform() and
    QPainter::setWorldTransform() functions. You can at any time save the
    QPainter's transformation matrix by calling the QPainter::save()
    function which saves the matrix on an internal stack. The
    QPainter::restore() function pops it back.

    One frequent need for the transformation matrix is when reusing
    the same drawing code on a variety of paint devices. Without
    transformations, the results are tightly bound to the resolution
    of the paint device. Printers have high resolution, e.g. 600 dots
    per inch, whereas screens often have between 72 and 100 dots per
    inch.

    \table 100%
    \header
    \o {2,1} Analog Clock Example
    \row
    \o \inlineimage coordinatesystem-analogclock.png
    \o
    The Analog Clock example shows how to draw the contents of a
    custom widget using QPainter's transformation matrix.

    Qt's example directory provides a complete walk-through of the
    example. Here, we will only review the example's \l
    {QWidget::paintEvent()}{paintEvent()} function to see how we can
    use the transformation matrix (i.e. QPainter's matrix functions)
    to draw the clock's face.

    We recommend compiling and running this example before you read
    any further. In particular, try resizing the window to different
    sizes.

    \row
    \o {2,1}

    \snippet examples/widgets/analogclock/analogclock.cpp 9

    First, we set up the painter. We translate the coordinate system
    so that point (0, 0) is in the widget's center, instead of being
    at the top-left corner. We also scale the system by \c side / 100,
    where \c side is either the widget's width or the height,
    whichever is shortest. We want the clock to be square, even if the
    device isn't.

    This will give us a 200 x 200 square area, with the origin (0, 0)
    in the center, that we can draw on. What we draw will show up in
    the largest possible square that will fit in the widget.

    See also the \l {Window-Viewport Conversion} section.

    \snippet examples/widgets/analogclock/analogclock.cpp 18

    We draw the clock's hour hand by rotating the coordinate system
    and calling QPainter::drawConvexPolygon(). Thank's to the
    rotation, it's drawn pointed in the right direction.

    The polygon is specified as an array of alternating \e x, \e y
    values, stored in the \c hourHand static variable (defined at the
    beginning of the function), which corresponds to the four points
    (2, 0), (0, 2), (-2, 0), and (0, -25).

    The calls to QPainter::save() and QPainter::restore() surrounding
    the code guarantees that the code that follows won't be disturbed
    by the transformations we've used.

    \snippet examples/widgets/analogclock/analogclock.cpp 24

    We do the same for the clock's minute hand, which is defined by
    the four points (1, 0), (0, 1), (-1, 0), and (0, -40). These
    coordinates specify a hand that is thinner and longer than the
    minute hand.

    \snippet examples/widgets/analogclock/analogclock.cpp 27

    Finally, we draw the clock face, which consists of twelve short
    lines at 30-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.
    \endtable

    For a demonstation of Qt's ability to perform affine
    transformations on painting operations, see the \l
    {demos/affine}{Affine Transformations} demo which allows the user
    to experiment with the transformation operations.  See also the \l
    {painting/transformations}{Transformations} example which shows
    how transformations influence the way that QPainter renders
    graphics primitives. In particular, it shows how the order of
    transformations affects the result.

    For more information about the transformation matrix, see the
    QTransform documentation.

    \section1 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 \l
    {QPainter::worldTransform()}{worldTransform()} (described in the \l
    Transformations section), and QPainter's \l
    {QPainter::viewport()}{viewport()} and \l
    {QPainter::window()}{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:

    \snippet doc/src/snippets/code/doc_src_coordsys.qdoc 4

    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:

    \snippet doc/src/snippets/code/doc_src_coordsys.qdoc 5

    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.

    \image coordinatesystem-transformations.png

    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.

    \omit
    \section1 Related Classes

    Qt's paint system, Arthur, is primarily based on the QPainter,
    QPaintDevice, and QPaintEngine classes:

    \table
    \header \o Class \o Description
    \row
    \o QPainter
    \o
    The QPainter class performs low-level painting on widgets and
    other paint devices.  QPainter can operate on any object that
    inherits the QPaintDevice class, using the same code.
    \row
    \o QPaintDevice
    \o
    The QPaintDevice class is the base class of objects that can be
    painted. Qt provides several devices: QWidget, QImage, QPixmap,
    QPrinter and QPicture, and other devices can also be defined by
    subclassing QPaintDevice.
    \row
    \o QPaintEngine
    \o
    The QPaintEngine class provides an abstract definition of how
    QPainter draws to a given device on a given platform.  Qt 4
    provides several premade implementations of QPaintEngine for the
    different painter backends we support; it provides one paint
    engine for each supported window system and painting
    frameworkt. You normally don't need to use this class directly.
    \endtable

    The 2D transformations of the coordinate system are specified
    using the QTransform class:

    \table
    \header \o Class \o Description
    \row
    \o QTransform
    \o
    A 3 x 3 transformation matrix. Use QTransform to rotate, shear,
    scale, or translate the coordinate system.
    \endtable

    In addition Qt provides several graphics primitive classes. Some
    of these classes exist in two versions: an \c{int}-based version
    and a \c{qreal}-based version. For these, the \c qreal version's
    name is suffixed with an \c F.

    \table
    \header \o Class \o Description
    \row
    \o \l{QPoint}(\l{QPointF}{F})
    \o
    A single 2D point in the coordinate system. Most functions in Qt
    that deal with points can accept either a QPoint, a QPointF, two
    \c{int}s, or two \c{qreal}s.
    \row
    \o \l{QSize}(\l{QSizeF}{F})
    \o
    A single 2D vector. Internally, QPoint and QSize are the same, but
    a point is not the same as a size, so both classes exist.  Again,
    most functions accept either QSizeF, a QSize, two \c{int}s, or two
    \c{qreal}s.
    \row
    \o \l{QRect}(\l{QRectF}{F})
    \o
    A 2D rectangle. Most functions accept either a QRectF, a QRect,
    four \c{int}s, or four \c {qreal}s.
    \row
    \o \l{QLine}(\l{QLineF}{F})
    \o
    A 2D finite-length line, characterized by a start point and an end
    point.
    \row
    \o \l{QPolygon}(\l{QPolygonF}{F})
    \o
    A 2D polygon. A polygon is a vector of \c{QPoint(F)}s. If the
    first and last points are the same, the polygon is closed.
    \row
    \o QPainterPath
    \o
    A vectorial specification of a 2D shape. Painter paths are the
    ultimate painting primitive, in the sense that any shape
    (rectange, ellipse, spline) or combination of shapes can be
    expressed as a path. A path specifies both an outline and an area.
    \row
    \o QRegion
    \o
    An area in a paint device, expressed as a list of
    \l{QRect}s. In general, we recommend using the vectorial
    QPainterPath class instead of QRegion for specifying areas,
    because QPainterPath handles painter transformations much better.
    \endtable
    \endomit

    \sa {Analog Clock Example}, {Transformations Example}
*/
