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Branched from the monolithic repo, Qt master branch, at commit
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diff --git a/src/gui/painting/qmatrix.cpp b/src/gui/painting/qmatrix.cpp
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+/****************************************************************************
+**
+** Copyright (C) 2011 Nokia Corporation and/or its subsidiary(-ies).
+** All rights reserved.
+** Contact: Nokia Corporation (qt-info@nokia.com)
+**
+** This file is part of the QtGui module of the Qt Toolkit.
+**
+** $QT_BEGIN_LICENSE:LGPL$
+** No Commercial Usage
+** This file contains pre-release code and may not be distributed.
+** You may use this file in accordance with the terms and conditions
+** contained in the Technology Preview License Agreement accompanying
+** this package.
+**
+** GNU Lesser General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU Lesser
+** General Public License version 2.1 as published by the Free Software
+** Foundation and appearing in the file LICENSE.LGPL included in the
+** packaging of this file.  Please review the following information to
+** ensure the GNU Lesser General Public License version 2.1 requirements
+** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
+**
+** In addition, as a special exception, Nokia gives you certain additional
+** rights.  These rights are described in the Nokia Qt LGPL Exception
+** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.
+**
+** If you have questions regarding the use of this file, please contact
+** Nokia at qt-info@nokia.com.
+**
+**
+**
+**
+**
+**
+**
+**
+** $QT_END_LICENSE$
+**
+****************************************************************************/
+
+#include "qdatastream.h"
+#include "qdebug.h"
+#include "qmatrix.h"
+#include "qregion.h"
+#include "qpainterpath.h"
+#include "qvariant.h"
+#include <qmath.h>
+
+#include <limits.h>
+
+QT_BEGIN_NAMESPACE
+
+/*!
+    \class QMatrix
+    \brief The QMatrix class specifies 2D transformations of a
+    coordinate system.
+    \obsolete
+
+    \ingroup painting
+
+    A matrix specifies how to translate, scale, shear or rotate the
+    coordinate system, and is typically used when rendering graphics.
+    QMatrix, in contrast to QTransform, does not allow perspective
+    transformations. QTransform is the recommended transformation
+    class in Qt.
+
+    A QMatrix object can be built using the setMatrix(), scale(),
+    rotate(), translate() and shear() functions.  Alternatively, it
+    can be built by applying \l {QMatrix#Basic Matrix
+    Operations}{basic matrix operations}. The matrix can also be
+    defined when constructed, and it can be reset to the identity
+    matrix (the default) using the reset() function.
+
+    The QMatrix class supports mapping of graphic primitives: A given
+    point, line, polygon, region, or painter path can be mapped to the
+    coordinate system defined by \e this matrix using the map()
+    function. In case of a rectangle, its coordinates can be
+    transformed using the mapRect() function. A rectangle can also be
+    transformed into a \e polygon (mapped to the coordinate system
+    defined by \e this matrix), using the mapToPolygon() function.
+
+    QMatrix provides the isIdentity() function which returns true if
+    the matrix is the identity matrix, and the isInvertible() function
+    which returns true if the matrix is non-singular (i.e. AB = BA =
+    I). The inverted() function returns an inverted copy of \e this
+    matrix if it is invertible (otherwise it returns the identity
+    matrix). In addition, QMatrix provides the determinant() function
+    returning the matrix's determinant.
+
+    Finally, the QMatrix class supports matrix multiplication, and
+    objects of the class can be streamed as well as compared.
+
+    \tableofcontents
+
+    \section1 Rendering Graphics
+
+    When rendering graphics, the matrix defines the transformations
+    but the actual transformation is performed by the drawing routines
+    in QPainter.
+
+    By default, QPainter operates on the associated device's own
+    coordinate system.  The standard coordinate system of a
+    QPaintDevice has its origin located at the top-left position. The
+    \e x values increase to the right; \e y values increase
+    downward. For a complete description, see the \l {Coordinate
+    System}{coordinate system} documentation.
+
+    QPainter has functions to translate, scale, shear and rotate the
+    coordinate system without using a QMatrix. For example:
+
+    \table 100%
+    \row
+    \o \inlineimage qmatrix-simpletransformation.png
+    \o
+    \snippet doc/src/snippets/matrix/matrix.cpp 0
+    \endtable
+
+    Although these functions are very convenient, it can be more
+    efficient to build a QMatrix and call QPainter::setMatrix() if you
+    want to perform more than a single transform operation. For
+    example:
+
+    \table 100%
+    \row
+    \o \inlineimage qmatrix-combinedtransformation.png
+    \o
+    \snippet doc/src/snippets/matrix/matrix.cpp 1
+    \endtable
+
+    \section1 Basic Matrix Operations
+
+    \image qmatrix-representation.png
+
+    A QMatrix object contains a 3 x 3 matrix.  The \c dx and \c dy
+    elements specify horizontal and vertical translation. The \c m11
+    and \c m22 elements specify horizontal and vertical scaling. And
+    finally, the \c m21 and \c m12 elements specify horizontal and
+    vertical \e shearing.
+
+    QMatrix transforms a point in the plane to another point using the
+    following formulas:
+
+    \snippet doc/src/snippets/code/src_gui_painting_qmatrix.cpp 0
+
+    The point \e (x, y) is the original point, and \e (x', y') is the
+    transformed point. \e (x', y') can be transformed back to \e (x,
+    y) by performing the same operation on the inverted() matrix.
+
+    The various matrix elements can be set when constructing the
+    matrix, or by using the setMatrix() function later on. They can also
+    be manipulated using the translate(), rotate(), scale() and
+    shear() convenience functions, The currently set values can be
+    retrieved using the m11(), m12(), m21(), m22(), dx() and dy()
+    functions.
+
+    Translation is the simplest transformation. Setting \c dx and \c
+    dy will move the coordinate system \c dx units along the X axis
+    and \c dy units along the Y axis.  Scaling can be done by setting
+    \c m11 and \c m22. For example, setting \c m11 to 2 and \c m22 to
+    1.5 will double the height and increase the width by 50%.  The
+    identity matrix has \c m11 and \c m22 set to 1 (all others are set
+    to 0) mapping a point to itself. Shearing is controlled by \c m12
+    and \c m21. Setting these elements to values different from zero
+    will twist the coordinate system. Rotation is achieved by
+    carefully setting both the shearing factors and the scaling
+    factors.
+
+    Here's the combined transformations example using basic matrix
+    operations:
+
+    \table 100%
+    \row
+    \o \inlineimage qmatrix-combinedtransformation.png
+    \o
+    \snippet doc/src/snippets/matrix/matrix.cpp 2
+    \endtable
+
+    \sa QPainter, QTransform, {Coordinate System}, 
+    {demos/affine}{Affine Transformations Demo}, {Transformations Example}
+*/
+
+
+// some defines to inline some code
+#define MAPDOUBLE(x, y, nx, ny) \
+{ \
+    qreal fx = x; \
+    qreal fy = y; \
+    nx = _m11*fx + _m21*fy + _dx; \
+    ny = _m12*fx + _m22*fy + _dy; \
+}
+
+#define MAPINT(x, y, nx, ny) \
+{ \
+    qreal fx = x; \
+    qreal fy = y; \
+    nx = qRound(_m11*fx + _m21*fy + _dx); \
+    ny = qRound(_m12*fx + _m22*fy + _dy); \
+}
+
+/*****************************************************************************
+  QMatrix member functions
+ *****************************************************************************/
+/*!
+    \fn QMatrix::QMatrix(Qt::Initialization)
+    \internal
+*/
+
+/*!
+    Constructs an identity matrix.
+
+    All elements are set to zero except \c m11 and \c m22 (specifying
+    the scale), which are set to 1.
+
+    \sa reset()
+*/
+
+QMatrix::QMatrix()
+    : _m11(1.)
+    , _m12(0.)
+    , _m21(0.)
+    , _m22(1.)
+    , _dx(0.)
+    , _dy(0.)
+{
+}
+
+/*!
+    Constructs a matrix with the elements, \a m11, \a m12, \a m21, \a
+    m22, \a dx and \a dy.
+
+    \sa setMatrix()
+*/
+
+QMatrix::QMatrix(qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)
+    : _m11(m11)
+    , _m12(m12)
+    , _m21(m21)
+    , _m22(m22)
+    , _dx(dx)
+    , _dy(dy)
+{
+}
+
+
+/*!
+     Constructs a matrix that is a copy of the given \a matrix.
+ */
+QMatrix::QMatrix(const QMatrix &matrix)
+    : _m11(matrix._m11)
+    , _m12(matrix._m12)
+    , _m21(matrix._m21)
+    , _m22(matrix._m22)
+    , _dx(matrix._dx)
+    , _dy(matrix._dy)
+{
+}
+
+/*!
+    Sets the matrix elements to the specified values, \a m11, \a m12,
+    \a m21, \a m22, \a dx and \a dy.
+
+    Note that this function replaces the previous values. QMatrix
+    provide the translate(), rotate(), scale() and shear() convenience
+    functions to manipulate the various matrix elements based on the
+    currently defined coordinate system.
+
+    \sa QMatrix()
+*/
+
+void QMatrix::setMatrix(qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)
+{
+    _m11 = m11;
+    _m12 = m12;
+    _m21 = m21;
+    _m22 = m22;
+    _dx  = dx;
+    _dy  = dy;
+}
+
+
+/*!
+    \fn qreal QMatrix::m11() const
+
+    Returns the horizontal scaling factor.
+
+    \sa scale(), {QMatrix#Basic Matrix Operations}{Basic Matrix
+    Operations}
+*/
+
+/*!
+    \fn qreal QMatrix::m12() const
+
+    Returns the vertical shearing factor.
+
+    \sa shear(), {QMatrix#Basic Matrix Operations}{Basic Matrix
+    Operations}
+*/
+
+/*!
+    \fn qreal QMatrix::m21() const
+
+    Returns the horizontal shearing factor.
+
+    \sa shear(), {QMatrix#Basic Matrix Operations}{Basic Matrix
+    Operations}
+*/
+
+/*!
+    \fn qreal QMatrix::m22() const
+
+    Returns the vertical scaling factor.
+
+    \sa scale(), {QMatrix#Basic Matrix Operations}{Basic Matrix
+    Operations}
+*/
+
+/*!
+    \fn qreal QMatrix::dx() const
+
+    Returns the horizontal translation factor.
+
+    \sa translate(), {QMatrix#Basic Matrix Operations}{Basic Matrix
+    Operations}
+*/
+
+/*!
+    \fn qreal QMatrix::dy() const
+
+    Returns the vertical translation factor.
+
+    \sa translate(), {QMatrix#Basic Matrix Operations}{Basic Matrix
+    Operations}
+*/
+
+
+/*!
+    Maps the given coordinates \a x and \a y into the coordinate
+    system defined by this matrix. The resulting values are put in *\a
+    tx and *\a ty, respectively.
+
+    The coordinates are transformed using the following formulas:
+
+    \snippet doc/src/snippets/code/src_gui_painting_qmatrix.cpp 1
+
+    The point (x, y) is the original point, and (x', y') is the
+    transformed point.
+
+    \sa {QMatrix#Basic Matrix Operations}{Basic Matrix Operations}
+*/
+
+void QMatrix::map(qreal x, qreal y, qreal *tx, qreal *ty) const
+{
+    MAPDOUBLE(x, y, *tx, *ty);
+}
+
+
+
+/*!
+    \overload
+
+    Maps the given coordinates \a x and \a y into the coordinate
+    system defined by this matrix. The resulting values are put in *\a
+    tx and *\a ty, respectively. Note that the transformed coordinates
+    are rounded to the nearest integer.
+*/
+
+void QMatrix::map(int x, int y, int *tx, int *ty) const
+{
+    MAPINT(x, y, *tx, *ty);
+}
+
+QRect QMatrix::mapRect(const QRect &rect) const
+{
+    QRect result;
+    if (_m12 == 0.0F && _m21 == 0.0F) {
+        int x = qRound(_m11*rect.x() + _dx);
+        int y = qRound(_m22*rect.y() + _dy);
+        int w = qRound(_m11*rect.width());
+        int h = qRound(_m22*rect.height());
+        if (w < 0) {
+            w = -w;
+            x -= w;
+        }
+        if (h < 0) {
+            h = -h;
+            y -= h;
+        }
+        result = QRect(x, y, w, h);
+    } else {
+        // see mapToPolygon for explanations of the algorithm.
+        qreal x0, y0;
+        qreal x, y;
+        MAPDOUBLE(rect.left(), rect.top(), x0, y0);
+        qreal xmin = x0;
+        qreal ymin = y0;
+        qreal xmax = x0;
+        qreal ymax = y0;
+        MAPDOUBLE(rect.right() + 1, rect.top(), x, y);
+        xmin = qMin(xmin, x);
+        ymin = qMin(ymin, y);
+        xmax = qMax(xmax, x);
+        ymax = qMax(ymax, y);
+        MAPDOUBLE(rect.right() + 1, rect.bottom() + 1, x, y);
+        xmin = qMin(xmin, x);
+        ymin = qMin(ymin, y);
+        xmax = qMax(xmax, x);
+        ymax = qMax(ymax, y);
+        MAPDOUBLE(rect.left(), rect.bottom() + 1, x, y);
+        xmin = qMin(xmin, x);
+        ymin = qMin(ymin, y);
+        xmax = qMax(xmax, x);
+        ymax = qMax(ymax, y);
+        result = QRect(qRound(xmin), qRound(ymin), qRound(xmax)-qRound(xmin), qRound(ymax)-qRound(ymin));
+    }
+    return result;
+}
+
+/*!
+    \fn QRectF QMatrix::mapRect(const QRectF &rectangle) const
+
+    Creates and returns a QRectF object that is a copy of the given \a
+    rectangle, mapped into the coordinate system defined by this
+    matrix.
+
+    The rectangle's coordinates are transformed using the following
+    formulas:
+
+    \snippet doc/src/snippets/code/src_gui_painting_qmatrix.cpp 2
+
+    If rotation or shearing has been specified, this function returns
+    the \e bounding rectangle. To retrieve the exact region the given
+    \a rectangle maps to, use the mapToPolygon() function instead.
+
+    \sa mapToPolygon(), {QMatrix#Basic Matrix Operations}{Basic Matrix
+    Operations}
+*/
+QRectF QMatrix::mapRect(const QRectF &rect) const
+{
+    QRectF result;
+    if (_m12 == 0.0F && _m21 == 0.0F) {
+        qreal x = _m11*rect.x() + _dx;
+        qreal y = _m22*rect.y() + _dy;
+        qreal w = _m11*rect.width();
+        qreal h = _m22*rect.height();
+        if (w < 0) {
+            w = -w;
+            x -= w;
+        }
+        if (h < 0) {
+            h = -h;
+            y -= h;
+        }
+        result = QRectF(x, y, w, h);
+    } else {
+        qreal x0, y0;
+        qreal x, y;
+        MAPDOUBLE(rect.x(), rect.y(), x0, y0);
+        qreal xmin = x0;
+        qreal ymin = y0;
+        qreal xmax = x0;
+        qreal ymax = y0;
+        MAPDOUBLE(rect.x() + rect.width(), rect.y(), x, y);
+        xmin = qMin(xmin, x);
+        ymin = qMin(ymin, y);
+        xmax = qMax(xmax, x);
+        ymax = qMax(ymax, y);
+        MAPDOUBLE(rect.x() + rect.width(), rect.y() + rect.height(), x, y);
+        xmin = qMin(xmin, x);
+        ymin = qMin(ymin, y);
+        xmax = qMax(xmax, x);
+        ymax = qMax(ymax, y);
+        MAPDOUBLE(rect.x(), rect.y() + rect.height(), x, y);
+        xmin = qMin(xmin, x);
+        ymin = qMin(ymin, y);
+        xmax = qMax(xmax, x);
+        ymax = qMax(ymax, y);
+        result = QRectF(xmin, ymin, xmax-xmin, ymax - ymin);
+    }
+    return result;
+}
+
+/*!
+    \fn QRect QMatrix::mapRect(const QRect &rectangle) const
+    \overload
+
+    Creates and returns a QRect object that is a copy of the given \a
+    rectangle, mapped into the coordinate system defined by this
+    matrix. Note that the transformed coordinates are rounded to the
+    nearest integer.
+*/
+
+
+/*!
+    \fn QPoint operator*(const QPoint &point, const QMatrix &matrix)
+    \relates QMatrix
+
+    This is the same as \a{matrix}.map(\a{point}).
+
+    \sa QMatrix::map()
+*/
+
+QPoint QMatrix::map(const QPoint &p) const
+{
+    qreal fx = p.x();
+    qreal fy = p.y();
+    return QPoint(qRound(_m11*fx + _m21*fy + _dx),
+                   qRound(_m12*fx + _m22*fy + _dy));
+}
+
+/*!
+    \fn QPointF operator*(const QPointF &point, const QMatrix &matrix)
+    \relates QMatrix
+
+    Same as \a{matrix}.map(\a{point}).
+
+    \sa QMatrix::map()
+*/
+
+/*!
+    \overload
+
+    Creates and returns a QPointF object that is a copy of the given
+    \a point, mapped into the coordinate system defined by this
+    matrix.
+*/
+QPointF QMatrix::map(const QPointF &point) const
+{
+    qreal fx = point.x();
+    qreal fy = point.y();
+    return QPointF(_m11*fx + _m21*fy + _dx, _m12*fx + _m22*fy + _dy);
+}
+
+/*!
+    \fn QPoint QMatrix::map(const QPoint &point) const
+    \overload
+
+    Creates and returns a QPoint object that is a copy of the given \a
+    point, mapped into the coordinate system defined by this
+    matrix. Note that the transformed coordinates are rounded to the
+    nearest integer.
+*/
+
+/*!
+    \fn QLineF operator*(const QLineF &line, const QMatrix &matrix)
+    \relates QMatrix
+
+    This is the same as \a{matrix}.map(\a{line}).
+
+    \sa QMatrix::map()
+*/
+
+/*!
+    \fn QLine operator*(const QLine &line, const QMatrix &matrix)
+    \relates QMatrix
+
+    This is the same as \a{matrix}.map(\a{line}).
+
+    \sa QMatrix::map()
+*/
+
+/*!
+    \overload
+
+    Creates and returns a QLineF object that is a copy of the given \a
+    line, mapped into the coordinate system defined by this matrix.
+*/
+QLineF QMatrix::map(const QLineF &line) const
+{
+    return QLineF(map(line.p1()), map(line.p2()));
+}
+
+/*!
+    \overload
+
+    Creates and returns a QLine object that is a copy of the given \a
+    line, mapped into the coordinate system defined by this matrix.
+    Note that the transformed coordinates are rounded to the nearest
+    integer.
+*/
+QLine QMatrix::map(const QLine &line) const
+{
+    return QLine(map(line.p1()), map(line.p2()));
+}
+
+/*!
+    \fn QPolygonF operator *(const QPolygonF &polygon, const QMatrix &matrix)
+    \relates QMatrix
+
+    This is the same as \a{matrix}.map(\a{polygon}).
+
+    \sa QMatrix::map()
+*/
+
+/*!
+    \fn QPolygon operator*(const QPolygon &polygon, const QMatrix &matrix)
+    \relates QMatrix
+
+    This is the same as \a{matrix}.map(\a{polygon}).
+
+    \sa QMatrix::map()
+*/
+
+QPolygon QMatrix::map(const QPolygon &a) const
+{
+    int size = a.size();
+    int i;
+    QPolygon p(size);
+    const QPoint *da = a.constData();
+    QPoint *dp = p.data();
+    for(i = 0; i < size; i++) {
+        MAPINT(da[i].x(), da[i].y(), dp[i].rx(), dp[i].ry());
+    }
+    return p;
+}
+
+/*!
+    \fn QPolygonF QMatrix::map(const QPolygonF &polygon) const
+    \overload
+
+    Creates and returns a QPolygonF object that is a copy of the given
+    \a polygon, mapped into the coordinate system defined by this
+    matrix.
+*/
+QPolygonF QMatrix::map(const QPolygonF &a) const
+{
+    int size = a.size();
+    int i;
+    QPolygonF p(size);
+    const QPointF *da = a.constData();
+    QPointF *dp = p.data();
+    for(i = 0; i < size; i++) {
+        MAPDOUBLE(da[i].xp, da[i].yp, dp[i].xp, dp[i].yp);
+    }
+    return p;
+}
+
+/*!
+    \fn QPolygon QMatrix::map(const QPolygon &polygon) const
+    \overload
+
+    Creates and returns a QPolygon object that is a copy of the given
+    \a polygon, mapped into the coordinate system defined by this
+    matrix. Note that the transformed coordinates are rounded to the
+    nearest integer.
+*/
+
+/*!
+    \fn QRegion operator*(const QRegion &region, const QMatrix &matrix)
+    \relates QMatrix
+
+    This is the same as \a{matrix}.map(\a{region}).
+
+    \sa QMatrix::map()
+*/
+
+extern QPainterPath qt_regionToPath(const QRegion &region);
+
+/*!
+    \fn QRegion QMatrix::map(const QRegion &region) const
+    \overload
+
+    Creates and returns a QRegion object that is a copy of the given
+    \a region, mapped into the coordinate system defined by this matrix.
+
+    Calling this method can be rather expensive if rotations or
+    shearing are used.
+*/
+QRegion QMatrix::map(const QRegion &r) const
+{
+    if (_m11 == 1.0 && _m22 == 1.0 && _m12 == 0.0 && _m21 == 0.0) { // translate or identity
+        if (_dx == 0.0 && _dy == 0.0) // Identity
+            return r;
+        QRegion copy(r);
+        copy.translate(qRound(_dx), qRound(_dy));
+        return copy;
+    }
+
+    QPainterPath p = map(qt_regionToPath(r));
+    return p.toFillPolygon().toPolygon();
+}
+
+/*!
+    \fn QPainterPath operator *(const QPainterPath &path, const QMatrix &matrix)
+    \relates QMatrix
+
+    This is the same as \a{matrix}.map(\a{path}).
+
+    \sa QMatrix::map()
+*/
+
+/*!
+    \overload
+
+    Creates and returns a QPainterPath object that is a copy of the
+    given \a path, mapped into the coordinate system defined by this
+    matrix.
+*/
+QPainterPath QMatrix::map(const QPainterPath &path) const
+{
+    if (path.isEmpty())
+        return QPainterPath();
+
+    QPainterPath copy = path;
+
+    // Translate or identity
+    if (_m11 == 1.0 && _m22 == 1.0 && _m12 == 0.0 && _m21 == 0.0) {
+
+        // Translate
+        if (_dx != 0.0 || _dy != 0.0) {
+            copy.detach();
+            for (int i=0; i<path.elementCount(); ++i) {
+                QPainterPath::Element &e = copy.d_ptr->elements[i];
+                e.x += _dx;
+                e.y += _dy;
+            }
+        }
+
+    // Full xform
+    } else {
+        copy.detach();
+        for (int i=0; i<path.elementCount(); ++i) {
+            QPainterPath::Element &e = copy.d_ptr->elements[i];
+            qreal fx = e.x, fy = e.y;
+            e.x = _m11*fx + _m21*fy + _dx;
+            e.y =  _m12*fx + _m22*fy + _dy;
+        }
+    }
+
+    return copy;
+}
+
+/*!
+    \fn QRegion QMatrix::mapToRegion(const QRect &rectangle) const
+
+    Returns the transformed rectangle \a rectangle as a QRegion
+    object. A rectangle which has been rotated or sheared may result
+    in a non-rectangular region being returned.
+
+    Use the mapToPolygon() or map() function instead.
+*/
+#ifdef QT3_SUPPORT
+QRegion QMatrix::mapToRegion(const QRect &rect) const
+{
+    QRegion result;
+    if (isIdentity()) {
+        result = rect;
+    } else if (m12() == 0.0F && m21() == 0.0F) {
+        int x = qRound(m11()*rect.x() + dx());
+        int y = qRound(m22()*rect.y() + dy());
+        int w = qRound(m11()*rect.width());
+        int h = qRound(m22()*rect.height());
+        if (w < 0) {
+            w = -w;
+            x -= w - 1;
+        }
+        if (h < 0) {
+            h = -h;
+            y -= h - 1;
+        }
+        result = QRect(x, y, w, h);
+    } else {
+        result = QRegion(mapToPolygon(rect));
+    }
+    return result;
+
+}
+#endif
+/*!
+    \fn QPolygon QMatrix::mapToPolygon(const QRect &rectangle) const
+
+    Creates and returns a QPolygon representation of the given \a
+    rectangle, mapped into the coordinate system defined by this
+    matrix.
+
+    The rectangle's coordinates are transformed using the following
+    formulas:
+
+    \snippet doc/src/snippets/code/src_gui_painting_qmatrix.cpp 3
+
+    Polygons and rectangles behave slightly differently when
+    transformed (due to integer rounding), so
+    \c{matrix.map(QPolygon(rectangle))} is not always the same as
+    \c{matrix.mapToPolygon(rectangle)}.
+
+    \sa mapRect(), {QMatrix#Basic Matrix Operations}{Basic Matrix
+    Operations}
+*/
+QPolygon QMatrix::mapToPolygon(const QRect &rect) const
+{
+    QPolygon a(4);
+    qreal x[4], y[4];
+    if (_m12 == 0.0F && _m21 == 0.0F) {
+        x[0] = _m11*rect.x() + _dx;
+        y[0] = _m22*rect.y() + _dy;
+        qreal w = _m11*rect.width();
+        qreal h = _m22*rect.height();
+        if (w < 0) {
+            w = -w;
+            x[0] -= w;
+        }
+        if (h < 0) {
+            h = -h;
+            y[0] -= h;
+        }
+        x[1] = x[0]+w;
+        x[2] = x[1];
+        x[3] = x[0];
+        y[1] = y[0];
+        y[2] = y[0]+h;
+        y[3] = y[2];
+    } else {
+        qreal right = rect.x() + rect.width();
+        qreal bottom = rect.y() + rect.height();
+        MAPDOUBLE(rect.x(), rect.y(), x[0], y[0]);
+        MAPDOUBLE(right, rect.y(), x[1], y[1]);
+        MAPDOUBLE(right, bottom, x[2], y[2]);
+        MAPDOUBLE(rect.x(), bottom, x[3], y[3]);
+    }
+#if 0
+    int i;
+    for(i = 0; i< 4; i++)
+        qDebug("coords(%d) = (%f/%f) (%d/%d)", i, x[i], y[i], qRound(x[i]), qRound(y[i]));
+    qDebug("width=%f, height=%f", qSqrt((x[1]-x[0])*(x[1]-x[0]) + (y[1]-y[0])*(y[1]-y[0])),
+            qSqrt((x[0]-x[3])*(x[0]-x[3]) + (y[0]-y[3])*(y[0]-y[3])));
+#endif
+    // all coordinates are correctly, tranform to a pointarray
+    // (rounding to the next integer)
+    a.setPoints(4, qRound(x[0]), qRound(y[0]),
+                 qRound(x[1]), qRound(y[1]),
+                 qRound(x[2]), qRound(y[2]),
+                 qRound(x[3]), qRound(y[3]));
+    return a;
+}
+
+/*!
+    Resets the matrix to an identity matrix, i.e. all elements are set
+    to zero, except \c m11 and \c m22 (specifying the scale) which are
+    set to 1.
+
+    \sa QMatrix(), isIdentity(), {QMatrix#Basic Matrix
+    Operations}{Basic Matrix Operations}
+*/
+
+void QMatrix::reset()
+{
+    _m11 = _m22 = 1.0;
+    _m12 = _m21 = _dx = _dy = 0.0;
+}
+
+/*!
+    \fn bool QMatrix::isIdentity() const
+
+    Returns true if the matrix is the identity matrix, otherwise
+    returns false.
+
+    \sa reset()
+*/
+
+/*!
+    Moves the coordinate system \a dx along the x axis and \a dy along
+    the y axis, and returns a reference to the matrix.
+
+    \sa setMatrix()
+*/
+
+QMatrix &QMatrix::translate(qreal dx, qreal dy)
+{
+    _dx += dx*_m11 + dy*_m21;
+    _dy += dy*_m22 + dx*_m12;
+    return *this;
+}
+
+/*!
+    \fn QMatrix &QMatrix::scale(qreal sx, qreal sy)
+
+    Scales the coordinate system by \a sx horizontally and \a sy
+    vertically, and returns a reference to the matrix.
+
+    \sa setMatrix()
+*/
+
+QMatrix &QMatrix::scale(qreal sx, qreal sy)
+{
+    _m11 *= sx;
+    _m12 *= sx;
+    _m21 *= sy;
+    _m22 *= sy;
+    return *this;
+}
+
+/*!
+    Shears the coordinate system by \a sh horizontally and \a sv
+    vertically, and returns a reference to the matrix.
+
+    \sa setMatrix()
+*/
+
+QMatrix &QMatrix::shear(qreal sh, qreal sv)
+{
+    qreal tm11 = sv*_m21;
+    qreal tm12 = sv*_m22;
+    qreal tm21 = sh*_m11;
+    qreal tm22 = sh*_m12;
+    _m11 += tm11;
+    _m12 += tm12;
+    _m21 += tm21;
+    _m22 += tm22;
+    return *this;
+}
+
+const qreal deg2rad = qreal(0.017453292519943295769);        // pi/180
+
+/*!
+    \fn QMatrix &QMatrix::rotate(qreal degrees)
+
+    Rotates the coordinate system the given \a degrees
+    counterclockwise.
+
+    Note that if you apply a QMatrix to a point defined in widget
+    coordinates, the direction of the rotation will be clockwise
+    because the y-axis points downwards.
+
+    Returns a reference to the matrix.
+
+    \sa setMatrix()
+*/
+
+QMatrix &QMatrix::rotate(qreal a)
+{
+    qreal sina = 0;
+    qreal cosa = 0;
+    if (a == 90. || a == -270.)
+        sina = 1.;
+    else if (a == 270. || a == -90.)
+        sina = -1.;
+    else if (a == 180.)
+        cosa = -1.;
+    else{
+        qreal b = deg2rad*a;                        // convert to radians
+        sina = qSin(b);               // fast and convenient
+        cosa = qCos(b);
+    }
+    qreal tm11 = cosa*_m11 + sina*_m21;
+    qreal tm12 = cosa*_m12 + sina*_m22;
+    qreal tm21 = -sina*_m11 + cosa*_m21;
+    qreal tm22 = -sina*_m12 + cosa*_m22;
+    _m11 = tm11; _m12 = tm12;
+    _m21 = tm21; _m22 = tm22;
+    return *this;
+}
+
+/*!
+    \fn bool QMatrix::isInvertible() const
+
+    Returns true if the matrix is invertible, otherwise returns false.
+
+    \sa inverted()
+*/
+
+/*!
+    \obsolete
+    \fn qreal QMatrix::det() const
+
+    Returns the matrix's determinant.
+
+    \sa determinant()
+*/
+
+/*!
+    \since 4.6
+    \fn qreal QMatrix::determinant() const
+
+    Returns the matrix's determinant.
+*/
+
+/*!
+    \fn QMatrix QMatrix::invert(bool *invertible) const
+
+    Returns an inverted copy of this matrix.
+
+    Use the inverted() function instead.
+*/
+
+/*!
+    Returns an inverted copy of this matrix.
+
+    If the matrix is singular (not invertible), the returned matrix is
+    the identity matrix. If \a invertible is valid (i.e. not 0), its
+    value is set to true if the matrix is invertible, otherwise it is
+    set to false.
+
+    \sa isInvertible()
+*/
+
+QMatrix QMatrix::inverted(bool *invertible) const
+{
+    qreal dtr = determinant();
+    if (dtr == 0.0) {
+        if (invertible)
+            *invertible = false;                // singular matrix
+        return QMatrix(true);
+    }
+    else {                                        // invertible matrix
+        if (invertible)
+            *invertible = true;
+        qreal dinv = 1.0/dtr;
+        return QMatrix((_m22*dinv),        (-_m12*dinv),
+                       (-_m21*dinv), (_m11*dinv),
+                       ((_m21*_dy - _m22*_dx)*dinv),
+                       ((_m12*_dx - _m11*_dy)*dinv),
+                       true);
+    }
+}
+
+
+/*!
+    \fn bool QMatrix::operator==(const QMatrix &matrix) const
+
+    Returns true if this matrix is equal to the given \a matrix,
+    otherwise returns false.
+*/
+
+bool QMatrix::operator==(const QMatrix &m) const
+{
+    return _m11 == m._m11 &&
+           _m12 == m._m12 &&
+           _m21 == m._m21 &&
+           _m22 == m._m22 &&
+           _dx == m._dx &&
+           _dy == m._dy;
+}
+
+/*!
+    \fn bool QMatrix::operator!=(const QMatrix &matrix) const
+
+    Returns true if this matrix is not equal to the given \a matrix,
+    otherwise returns false.
+*/
+
+bool QMatrix::operator!=(const QMatrix &m) const
+{
+    return _m11 != m._m11 ||
+           _m12 != m._m12 ||
+           _m21 != m._m21 ||
+           _m22 != m._m22 ||
+           _dx != m._dx ||
+           _dy != m._dy;
+}
+
+/*!
+    \fn QMatrix &QMatrix::operator *=(const QMatrix &matrix)
+    \overload
+
+    Returns the result of multiplying this matrix by the given \a
+    matrix.
+*/
+
+QMatrix &QMatrix::operator *=(const QMatrix &m)
+{
+    qreal tm11 = _m11*m._m11 + _m12*m._m21;
+    qreal tm12 = _m11*m._m12 + _m12*m._m22;
+    qreal tm21 = _m21*m._m11 + _m22*m._m21;
+    qreal tm22 = _m21*m._m12 + _m22*m._m22;
+
+    qreal tdx  = _dx*m._m11  + _dy*m._m21 + m._dx;
+    qreal tdy =  _dx*m._m12  + _dy*m._m22 + m._dy;
+
+    _m11 = tm11; _m12 = tm12;
+    _m21 = tm21; _m22 = tm22;
+    _dx = tdx; _dy = tdy;
+    return *this;
+}
+
+/*!
+    \fn QMatrix QMatrix::operator *(const QMatrix &matrix) const
+
+    Returns the result of multiplying this matrix by the given \a
+    matrix.
+
+    Note that matrix multiplication is not commutative, i.e. a*b !=
+    b*a.
+*/
+
+QMatrix QMatrix::operator *(const QMatrix &m) const
+{
+    qreal tm11 = _m11*m._m11 + _m12*m._m21;
+    qreal tm12 = _m11*m._m12 + _m12*m._m22;
+    qreal tm21 = _m21*m._m11 + _m22*m._m21;
+    qreal tm22 = _m21*m._m12 + _m22*m._m22;
+
+    qreal tdx  = _dx*m._m11  + _dy*m._m21 + m._dx;
+    qreal tdy =  _dx*m._m12  + _dy*m._m22 + m._dy;
+    return QMatrix(tm11, tm12, tm21, tm22, tdx, tdy, true);
+}
+
+/*!
+    Assigns the given \a matrix's values to this matrix.
+*/
+QMatrix &QMatrix::operator=(const QMatrix &matrix)
+{
+    _m11 = matrix._m11;
+    _m12 = matrix._m12;
+    _m21 = matrix._m21;
+    _m22 = matrix._m22;
+    _dx  = matrix._dx;
+    _dy  = matrix._dy;
+    return *this;
+}
+
+/*!
+    \since 4.2
+
+    Returns the matrix as a QVariant.
+*/
+QMatrix::operator QVariant() const
+{
+    return QVariant(QVariant::Matrix, this);
+}
+
+Q_GUI_EXPORT QPainterPath operator *(const QPainterPath &p, const QMatrix &m)
+{
+    return m.map(p);
+}
+
+
+/*****************************************************************************
+  QMatrix stream functions
+ *****************************************************************************/
+#ifndef QT_NO_DATASTREAM
+/*!
+    \fn QDataStream &operator<<(QDataStream &stream, const QMatrix &matrix)
+    \relates QMatrix
+
+    Writes the given \a matrix to the given \a stream and returns a
+    reference to the stream.
+
+    \sa {Serializing Qt Data Types}
+*/
+
+QDataStream &operator<<(QDataStream &s, const QMatrix &m)
+{
+    if (s.version() == 1) {
+        s << (float)m.m11() << (float)m.m12() << (float)m.m21()
+          << (float)m.m22() << (float)m.dx()  << (float)m.dy();
+    } else {
+        s << double(m.m11())
+          << double(m.m12())
+          << double(m.m21())
+          << double(m.m22())
+          << double(m.dx())
+          << double(m.dy());
+    }
+    return s;
+}
+
+/*!
+    \fn QDataStream &operator>>(QDataStream &stream, QMatrix &matrix)
+    \relates QMatrix
+
+    Reads the given \a matrix from the given \a stream and returns a
+    reference to the stream.
+
+    \sa {Serializing Qt Data Types}
+*/
+
+QDataStream &operator>>(QDataStream &s, QMatrix &m)
+{
+    if (s.version() == 1) {
+        float m11, m12, m21, m22, dx, dy;
+        s >> m11;  s >> m12;  s >> m21;  s >> m22;
+        s >> dx;   s >> dy;
+        m.setMatrix(m11, m12, m21, m22, dx, dy);
+    }
+    else {
+        double m11, m12, m21, m22, dx, dy;
+        s >> m11;
+        s >> m12;
+        s >> m21;
+        s >> m22;
+        s >> dx;
+        s >> dy;
+        m.setMatrix(m11, m12, m21, m22, dx, dy);
+    }
+    return s;
+}
+#endif // QT_NO_DATASTREAM
+
+#ifndef QT_NO_DEBUG_STREAM
+QDebug operator<<(QDebug dbg, const QMatrix &m)
+{
+    dbg.nospace() << "QMatrix("
+                  << "11=" << m.m11()
+                  << " 12=" << m.m12()
+                  << " 21=" << m.m21()
+                  << " 22=" << m.m22()
+                  << " dx=" << m.dx()
+                  << " dy=" << m.dy()
+                  << ')';
+    return dbg.space();
+}
+#endif
+
+/*!
+    \fn QRect QMatrix::map(const QRect &rect) const
+    \compat
+
+    Creates and returns a QRect object that is a copy of the given
+    rectangle, mapped into the coordinate system defined by this
+    matrix.
+
+    Use the mapRect() function instead.
+*/
+
+
+/*!
+    \fn bool qFuzzyCompare(const QMatrix& m1, const QMatrix& m2)
+
+    \relates QMatrix
+    \since 4.6
+
+    \brief The qFuzzyCompare function is for comparing two matrices
+    using a fuzziness factor.
+    
+    Returns true if \a m1 and \a m2 are equal, allowing for a small
+    fuzziness factor for floating-point comparisons; false otherwise.
+*/
+
+QT_END_NAMESPACE