Test conversion to TQt3 from Qt3 8c6fc1f8e35fd264dd01c582ca5e7549b32ab731

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diff --git a/src/kernel/qwmatrix.cpp b/src/kernel/qwmatrix.cpp
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+/****************************************************************************
+**
+** Implementation of TQWMatrix class
+**
+** Created : 941020
+**
+** Copyright (C) 1992-2008 Trolltech ASA.  All rights reserved.
+**
+** This file is part of the kernel module of the TQt GUI Toolkit.
+**
+** This file may be used under the terms of the GNU General
+** Public License versions 2.0 or 3.0 as published by the Free
+** Software Foundation and appearing in the files LICENSE.GPL2
+** and LICENSE.GPL3 included in the packaging of this file.
+** Alternatively you may (at your option) use any later version
+** of the GNU General Public License if such license has been
+** publicly approved by Trolltech ASA (or its successors, if any)
+** and the KDE Free TQt Foundation.
+**
+** Please review the following information to ensure GNU General
+** Public Licensing retquirements will be met:
+** http://trolltech.com/products/qt/licenses/licensing/opensource/.
+** If you are unsure which license is appropriate for your use, please
+** review the following information:
+** http://trolltech.com/products/qt/licenses/licensing/licensingoverview
+** or contact the sales department at [email protected].
+**
+** This file may be used under the terms of the Q Public License as
+** defined by Trolltech ASA and appearing in the file LICENSE.TQPL
+** included in the packaging of this file.  Licensees holding valid TQt
+** Commercial licenses may use this file in accordance with the TQt
+** Commercial License Agreement provided with the Software.
+**
+** This file is provided "AS IS" with NO WARRANTY OF ANY KIND,
+** INCLUDING THE WARRANTIES OF DESIGN, MERCHANTABILITY AND FITNESS FOR
+** A PARTICULAR PURPOSE. Trolltech reserves all rights not granted
+** herein.
+**
+**********************************************************************/
+
+#include "qwmatrix.h"
+#include "qdatastream.h"
+#include "qregion.h"
+#if defined(Q_WS_X11)
+double qsincos( double, bool calcCos );		// defined in qpainter_x11.cpp
+#else
+#include <math.h>
+#endif
+
+#include <limits.h>
+
+#ifndef QT_NO_WMATRIX
+
+/*!
+    \class TQWMatrix qwmatrix.h
+    \brief The TQWMatrix class specifies 2D transformations of a
+    coordinate system.
+
+    \ingroup graphics
+    \ingroup images
+
+    The standard coordinate system of a \link TQPaintDevice paint
+    device\endlink has the origin located at the top-left position. X
+    values increase to the right; Y values increase downward.
+
+    This coordinate system is the default for the TQPainter, which
+    renders graphics in a paint device. A user-defined coordinate
+    system can be specified by setting a TQWMatrix for the painter.
+
+    Example:
+    \code
+	MyWidget::paintEvent( TQPaintEvent * )
+	{
+            TQPainter p;                      // our painter
+            TQWMatrix m;                      // our transformation matrix
+            m.rotate( 22.5 );                // rotated coordinate system
+            p.begin( this );                 // start painting
+            p.setWorldMatrix( m );           // use rotated coordinate system
+            p.drawText( 30,20, "detator" );  // draw rotated text at 30,20
+            p.end();                         // painting done
+	}
+    \endcode
+
+    A matrix specifies how to translate, scale, shear or rotate the
+    graphics; the actual transformation is performed by the drawing
+    routines in TQPainter and by TQPixmap::xForm().
+
+    The TQWMatrix class contains a 3x3 matrix of the form:
+    <table align=center border=1 cellpadding=1 cellspacing=0>
+    <tr align=center><td>m11</td><td>m12</td><td>&nbsp;0 </td></tr>
+    <tr align=center><td>m21</td><td>m22</td><td>&nbsp;0 </td></tr>
+    <tr align=center><td>dx</td> <td>dy</td> <td>&nbsp;1 </td></tr>
+    </table>
+
+    A matrix transforms a point in the plane to another point:
+    \code
+	x' = m11*x + m21*y + dx
+	y' = m22*y + m12*x + dy
+    \endcode
+
+    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 \link
+    TQWMatrix::invert() inverted matrix\endlink.
+
+    The elements \e dx and \e dy specify horizontal and vertical
+    translation. The elements \e m11 and \e m22 specify horizontal and
+    vertical scaling. The elements \e m12 and \e m21 specify
+    horizontal and vertical shearing.
+
+    The identity matrix has \e m11 and \e m22 set to 1; all others are
+    set to 0. This matrix maps a point to itself.
+
+    Translation is the simplest transformation. Setting \e dx and \e
+    dy will move the coordinate system \e dx units along the X axis
+    and \e dy units along the Y axis.
+
+    Scaling can be done by setting \e m11 and \e m22. For example,
+    setting \e m11 to 2 and \e m22 to 1.5 will double the height and
+    increase the width by 50%.
+
+    Shearing is controlled by \e m12 and \e 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. The TQWMatrix also has a function
+    that sets \link rotate() rotation \endlink directly.
+
+    TQWMatrix lets you combine transformations like this:
+    \code
+	TQWMatrix m;           // identity matrix
+	m.translate(10, -20); // first translate (10,-20)
+	m.rotate(25);         // then rotate 25 degrees
+	m.scale(1.2, 0.7);    // finally scale it
+    \endcode
+
+    Here's the same example using basic matrix operations:
+    \code
+	double a    = pi/180 * 25;         // convert 25 to radians
+	double sina = sin(a);
+	double cosa = cos(a);
+	TQWMatrix m1(1, 0, 0, 1, 10, -20);  // translation matrix
+	TQWMatrix m2( cosa, sina,           // rotation matrix
+		    -sina, cosa, 0, 0 );
+	TQWMatrix m3(1.2, 0, 0, 0.7, 0, 0); // scaling matrix
+	TQWMatrix m;
+	m = m3 * m2 * m1;                  // combine all transformations
+    \endcode
+
+    \l TQPainter has functions to translate, scale, shear and rotate the
+    coordinate system without using a TQWMatrix. Although these
+    functions are very convenient, it can be more efficient to build a
+    TQWMatrix and call TQPainter::setWorldMatrix() if you want to perform
+    more than a single transform operation.
+
+    \sa TQPainter::setWorldMatrix(), TQPixmap::xForm()
+*/
+
+bool qt_old_transformations = TRUE;
+
+/*!
+    \enum TQWMatrix::TransformationMode
+
+    \keyword transformation matrix
+
+    TQWMatrix offers two transformation modes. Calculations can either
+    be done in terms of points (Points mode, the default), or in
+    terms of area (Area mode).
+
+    In Points mode the transformation is applied to the points that
+    mark out the shape's bounding line. In Areas mode the
+    transformation is applied in such a way that the area of the
+    contained region is correctly transformed under the matrix.
+
+    \value Points transformations are applied to the shape's points.
+    \value Areas transformations are applied (e.g. to the width and
+    height) so that the area is transformed.
+
+    Example:
+
+    Suppose we have a rectangle,
+    \c{TQRect( 10, 20, 30, 40 )} and a transformation matrix
+    \c{TQWMatrix( 2, 0, 0, 2, 0, 0 )} to double the rectangle's size.
+
+    In Points mode, the matrix will transform the top-left (10,20) and
+    the bottom-right (39,59) points producing a rectangle with its
+    top-left point at (20,40) and its bottom-right point at (78,118),
+    i.e. with a width of 59 and a height of 79.
+
+    In Areas mode, the matrix will transform the top-left point in
+    the same way as in Points mode to (20/40), and double the width
+    and height, so the bottom-right will become (69,99), i.e. a width
+    of 60 and a height of 80.
+
+    Because integer arithmetic is used (for speed), rounding
+    differences mean that the modes will produce slightly different
+    results given the same shape and the same transformation,
+    especially when scaling up. This also means that some operations
+    are not commutative.
+
+    Under Points mode, \c{matrix * ( region1 | region2 )} is not equal to
+    \c{matrix * region1 | matrix * region2}. Under Area mode, \c{matrix *
+    (pointarray[i])} is not neccesarily equal to
+    \c{(matrix * pointarry)[i]}.
+
+    \img xform.png Comparison of Points and Areas TransformationModes
+*/
+
+/*!
+    Sets the transformation mode that TQWMatrix and painter
+    transformations use to \a m.
+
+    \sa TQWMatrix::TransformationMode
+*/
+void TQWMatrix::setTransformationMode( TQWMatrix::TransformationMode m )
+{
+    if ( m == TQWMatrix::Points )
+	qt_old_transformations = TRUE;
+    else
+	qt_old_transformations = FALSE;
+}
+
+
+/*!
+    Returns the current transformation mode.
+
+    \sa TQWMatrix::TransformationMode
+*/
+TQWMatrix::TransformationMode TQWMatrix::transformationMode()
+{
+    return (qt_old_transformations ? TQWMatrix::Points : TQWMatrix::Areas );
+}
+
+
+// some defines to inline some code
+#define MAPDOUBLE( x, y, nx, ny ) \
+{ \
+    double fx = x; \
+    double fy = y; \
+    nx = _m11*fx + _m21*fy + _dx; \
+    ny = _m12*fx + _m22*fy + _dy; \
+}
+
+#define MAPINT( x, y, nx, ny ) \
+{ \
+    double fx = x; \
+    double fy = y; \
+    nx = qRound(_m11*fx + _m21*fy + _dx); \
+    ny = qRound(_m12*fx + _m22*fy + _dy); \
+}
+
+/*****************************************************************************
+  TQWMatrix member functions
+ *****************************************************************************/
+
+/*!
+    Constructs an identity matrix. All elements are set to zero except
+    \e m11 and \e m22 (scaling), which are set to 1.
+*/
+
+TQWMatrix::TQWMatrix()
+{
+    _m11 = _m22 = 1.0;
+    _m12 = _m21 = _dx = _dy = 0.0;
+}
+
+/*!
+    Constructs a matrix with the elements, \a m11, \a m12, \a m21, \a
+    m22, \a dx and \a dy.
+*/
+
+TQWMatrix::TQWMatrix( double m11, double m12, double m21, double m22,
+		    double dx, double dy )
+{
+    _m11 = m11;	 _m12 = m12;
+    _m21 = m21;	 _m22 = m22;
+    _dx	 = dx;	 _dy  = dy;
+}
+
+
+/*!
+    Sets the matrix elements to the specified values, \a m11, \a m12,
+    \a m21, \a m22, \a dx and \a dy.
+*/
+
+void TQWMatrix::setMatrix( double m11, double m12, double m21, double m22,
+			  double dx, double dy )
+{
+    _m11 = m11;	 _m12 = m12;
+    _m21 = m21;	 _m22 = m22;
+    _dx	 = dx;	 _dy  = dy;
+}
+
+
+/*!
+    \fn double TQWMatrix::m11() const
+
+    Returns the X scaling factor.
+*/
+
+/*!
+    \fn double TQWMatrix::m12() const
+
+    Returns the vertical shearing factor.
+*/
+
+/*!
+    \fn double TQWMatrix::m21() const
+
+    Returns the horizontal shearing factor.
+*/
+
+/*!
+    \fn double TQWMatrix::m22() const
+
+    Returns the Y scaling factor.
+*/
+
+/*!
+    \fn double TQWMatrix::dx() const
+
+    Returns the horizontal translation.
+*/
+
+/*!
+    \fn double TQWMatrix::dy() const
+
+    Returns the vertical translation.
+*/
+
+
+/*!
+    \overload
+
+    Transforms ( \a x, \a y ) to ( \a *tx, \a *ty ) using the
+    following formulae:
+
+    \code
+	*tx = m11*x + m21*y + dx
+	*ty = m22*y + m12*x + dy
+    \endcode
+*/
+
+void TQWMatrix::map( double x, double y, double *tx, double *ty ) const
+{
+    MAPDOUBLE( x, y, *tx, *ty );
+}
+
+/*!
+    Transforms ( \a x, \a y ) to ( \a *tx, \a *ty ) using the formulae:
+
+    \code
+	*tx = m11*x + m21*y + dx  (rounded to the nearest integer)
+	*ty = m22*y + m12*x + dy  (rounded to the nearest integer)
+    \endcode
+*/
+
+void TQWMatrix::map( int x, int y, int *tx, int *ty ) const
+{
+    MAPINT( x, y, *tx, *ty );
+}
+
+/*!
+    \fn TQPoint TQWMatrix::map( const TQPoint &p ) const
+
+    \overload
+
+    Transforms \a p to using the formulae:
+
+    \code
+	retx = m11*px + m21*py + dx  (rounded to the nearest integer)
+	rety = m22*py + m12*px + dy  (rounded to the nearest integer)
+    \endcode
+*/
+
+/*!
+  \fn TQRect TQWMatrix::map( const TQRect &r ) const
+
+  \obsolete
+
+  Please use \l TQWMatrix::mapRect() instead.
+
+  Note that this method does return the bounding rectangle of the \a r, when
+  shearing or rotations are used.
+*/
+
+/*!
+    \fn TQPointArray TQWMatrix::map( const TQPointArray &a ) const
+
+    \overload
+
+    Returns the point array \a a transformed by calling map for each point.
+*/
+
+
+/*!
+    \fn TQRegion TQWMatrix::map( const TQRegion &r ) const
+
+    \overload
+
+    Transforms the region \a r.
+
+    Calling this method can be rather expensive, if rotations or
+    shearing are used.
+*/
+
+/*!
+    \fn TQRegion TQWMatrix::mapToRegion( const TQRect &rect ) const
+
+    Returns the transformed rectangle \a rect.
+
+    A rectangle which has been rotated or sheared may result in a
+    non-rectangular region being returned.
+
+    Calling this method can be expensive, if rotations or shearing are
+    used. If you just need to know the bounding rectangle of the
+    returned region, use mapRect() which is a lot faster than this
+    function.
+
+    \sa TQWMatrix::mapRect()
+*/
+
+
+/*!
+    Returns the transformed rectangle \a rect.
+
+    The bounding rectangle is returned if rotation or shearing has
+    been specified.
+
+    If you need to know the exact region \a rect maps to use \l
+    operator*().
+
+    \sa operator*()
+*/
+
+TQRect TQWMatrix::mapRect( const TQRect &rect ) const
+{
+    TQRect result;
+    if( qt_old_transformations ) {
+	if ( _m12 == 0.0F && _m21 == 0.0F ) {
+	    result = TQRect( map(rect.topLeft()), map(rect.bottomRight()) ).normalize();
+	} else {
+	    TQPointArray a( rect );
+	    a = map( a );
+	    result = a.boundingRect();
+	}
+    } 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 = TQRect( x, y, w, h );
+	} else {
+
+	    // see mapToPolygon for explanations of the algorithm.
+	    double x0, y0;
+	    double x, y;
+	    MAPDOUBLE( rect.left(), rect.top(), x0, y0 );
+	    double xmin = x0;
+	    double ymin = y0;
+	    double xmax = x0;
+	    double ymax = y0;
+	    MAPDOUBLE( rect.right() + 1, rect.top(), x, y );
+	    xmin = TQMIN( xmin, x );
+	    ymin = TQMIN( ymin, y );
+	    xmax = TQMAX( xmax, x );
+	    ymax = TQMAX( ymax, y );
+	    MAPDOUBLE( rect.right() + 1, rect.bottom() + 1, x, y );
+	    xmin = TQMIN( xmin, x );
+	    ymin = TQMIN( ymin, y );
+	    xmax = TQMAX( xmax, x );
+	    ymax = TQMAX( ymax, y );
+	    MAPDOUBLE( rect.left(), rect.bottom() + 1, x, y );
+	    xmin = TQMIN( xmin, x );
+	    ymin = TQMIN( ymin, y );
+	    xmax = TQMAX( xmax, x );
+	    ymax = TQMAX( ymax, y );
+	    double w = xmax - xmin;
+	    double h = ymax - ymin;
+	    xmin -= ( xmin - x0 ) / w;
+	    ymin -= ( ymin - y0 ) / h;
+	    xmax -= ( xmax - x0 ) / w;
+	    ymax -= ( ymax - y0 ) / h;
+	    result = TQRect( qRound(xmin), qRound(ymin), qRound(xmax)-qRound(xmin)+1, qRound(ymax)-qRound(ymin)+1 );
+	}
+    }
+    return result;
+}
+
+
+/*!
+  \internal
+*/
+TQPoint TQWMatrix::operator *( const TQPoint &p ) const
+{
+    double fx = p.x();
+    double fy = p.y();
+    return TQPoint( qRound(_m11*fx + _m21*fy + _dx),
+		   qRound(_m12*fx + _m22*fy + _dy) );
+}
+
+
+struct TQWMDoublePoint {
+    double x;
+    double y;
+};
+
+/*!
+  \internal
+*/
+TQPointArray TQWMatrix::operator *( const TQPointArray &a ) const
+{
+    if( qt_old_transformations ) {
+	TQPointArray result = a.copy();
+	int x, y;
+	for ( int i=0; i<(int)result.size(); i++ ) {
+	    result.point( i, &x, &y );
+	    MAPINT( x, y, x, y );
+	    result.setPoint( i, x, y );
+	}
+	return result;
+    } else {
+	int size = a.size();
+	int i;
+	TQMemArray<TQWMDoublePoint> p( size );
+	TQPoint *da = a.data();
+	TQWMDoublePoint *dp = p.data();
+	double xmin = INT_MAX;
+	double ymin = xmin;
+	double xmax = INT_MIN;
+	double ymax = xmax;
+	int xminp = 0;
+	int yminp = 0;
+	for( i = 0; i < size; i++ ) {
+	    dp[i].x = da[i].x();
+	    dp[i].y = da[i].y();
+	    if ( dp[i].x < xmin ) {
+		xmin = dp[i].x;
+		xminp = i;
+	    }
+	    if ( dp[i].y < ymin ) {
+		ymin = dp[i].y;
+		yminp = i;
+	    }
+	    xmax = TQMAX( xmax, dp[i].x );
+	    ymax = TQMAX( ymax, dp[i].y );
+	}
+	double w = TQMAX( xmax - xmin, 1 );
+	double h = TQMAX( ymax - ymin, 1 );
+	for( i = 0; i < size; i++ ) {
+	    dp[i].x += (dp[i].x - xmin)/w;
+	    dp[i].y += (dp[i].y - ymin)/h;
+	    MAPDOUBLE( dp[i].x, dp[i].y, dp[i].x, dp[i].y );
+	}
+
+	// now apply correction back for transformed values...
+	xmin = INT_MAX;
+	ymin = xmin;
+	xmax = INT_MIN;
+	ymax = xmax;
+	for( i = 0; i < size; i++ ) {
+	    xmin = TQMIN( xmin, dp[i].x );
+	    ymin = TQMIN( ymin, dp[i].y );
+	    xmax = TQMAX( xmax, dp[i].x );
+	    ymax = TQMAX( ymax, dp[i].y );
+	}
+	w = TQMAX( xmax - xmin, 1 );
+	h = TQMAX( ymax - ymin, 1 );
+
+	TQPointArray result( size );
+	TQPoint *dr = result.data();
+	for( i = 0; i < size; i++ ) {
+	    dr[i].setX( qRound( dp[i].x - (dp[i].x - dp[xminp].x)/w ) );
+	    dr[i].setY( qRound( dp[i].y - (dp[i].y - dp[yminp].y)/h ) );
+	}
+	return result;
+    }
+}
+
+/*!
+\internal
+*/
+TQRegion TQWMatrix::operator * (const TQRect &rect ) const
+{
+    TQRegion result;
+    if ( isIdentity() ) {
+	result = rect;
+    } else if ( _m12 == 0.0F && _m21 == 0.0F ) {
+	if( qt_old_transformations ) {
+	    result = TQRect( map(rect.topLeft()), map(rect.bottomRight()) ).normalize();
+	} else {
+	    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 = TQRect( x, y, w, h );
+	}
+    } else {
+	result = TQRegion( mapToPolygon( rect ) );
+    }
+    return result;
+
+}
+
+/*!
+    Returns the transformed rectangle \a rect as a polygon.
+
+    Polygons and rectangles behave slightly differently
+    when transformed (due to integer rounding), so
+    \c{matrix.map( TQPointArray( rect ) )} is not always the same as
+    \c{matrix.mapToPolygon( rect )}.
+*/
+TQPointArray TQWMatrix::mapToPolygon( const TQRect &rect ) const
+{
+    TQPointArray a( 4 );
+    if ( qt_old_transformations ) {
+	a = TQPointArray( rect );
+	return operator *( a );
+    }
+    double x[4], y[4];
+    if ( _m12 == 0.0F && _m21 == 0.0F ) {
+	x[0] = qRound( _m11*rect.x() + _dx );
+        y[0] = qRound( _m22*rect.y() + _dy );
+	double w = qRound( _m11*rect.width() );
+	double h = qRound( _m22*rect.height() );
+	if ( w < 0 ) {
+	    w = -w;
+	    x[0] -= w - 1.;
+	}
+	if ( h < 0 ) {
+	    h = -h;
+	    y[0] -= h - 1.;
+	}
+	x[1] = x[0]+w-1;
+	x[2] = x[1];
+	x[3] = x[0];
+	y[1] = y[0];
+	y[2] = y[0]+h-1;
+	y[3] = y[2];
+    } else {
+	MAPINT( rect.left(), rect.top(), x[0], y[0] );
+	MAPINT( rect.right() + 1, rect.top(), x[1], y[1] );
+	MAPINT( rect.right() + 1, rect.bottom() + 1, x[2], y[2] );
+	MAPINT( rect.left(), rect.bottom() + 1, x[3], y[3] );
+
+	/*
+	Including rectangles as we have are evil.
+
+        We now have a rectangle that is one pixel to wide and one to
+        high. the tranformed position of the top-left corner is
+        correct. All other points need some adjustments.
+
+	Doing this mathematically exact would force us to calculate some square roots,
+	something we don't want for the sake of speed.
+
+        Instead we use an approximation, that converts to the correct
+        answer when m12 -> 0 and m21 -> 0, and accept smaller
+        errors in the general transformation case.
+
+        The solution is to calculate the width and height of the
+        bounding rect, and scale the points 1/2/3 by (xp-x0)/xw pixel direction
+        to point 0.
+        */
+
+	double xmin = x[0];
+	double ymin = y[0];
+	double xmax = x[0];
+	double ymax = y[0];
+	int i;
+	for( i = 1; i< 4; i++ ) {
+	    xmin = TQMIN( xmin, x[i] );
+	    ymin = TQMIN( ymin, y[i] );
+	    xmax = TQMAX( xmax, x[i] );
+	    ymax = TQMAX( ymax, y[i] );
+	}
+	double w = xmax - xmin;
+	double h = ymax - ymin;
+
+	for( i = 1; i < 4; i++ ) {
+	    x[i] -= (x[i] - x[0])/w;
+	    y[i] -= (y[i] - y[0])/h;
+	}
+    }
+#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", sqrt( (x[1]-x[0])*(x[1]-x[0]) + (y[1]-y[0])*(y[1]-y[0]) ),
+	    sqrt( (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;
+}
+
+/*!
+\internal
+*/
+TQRegion TQWMatrix::operator * (const TQRegion &r ) const
+{
+    if ( isIdentity() )
+	return r;
+    TQMemArray<TQRect> rects = r.rects();
+    TQRegion result;
+    register TQRect *rect = rects.data();
+    register int i = rects.size();
+    if ( _m12 == 0.0F && _m21 == 0.0F && _m11 > 1.0F && _m22 > 1.0F ) {
+	// simple case, no rotation
+	while ( i ) {
+	    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;
+	    }
+	    *rect = TQRect( x, y, w, h );
+	    rect++;
+	    i--;
+	}
+	result.setRects( rects.data(), rects.size() );
+    } else {
+	while ( i ) {
+	    result |= operator *( *rect );
+	    rect++;
+	    i--;
+	}
+    }
+    return result;
+}
+
+/*!
+    Resets the matrix to an identity matrix.
+
+    All elements are set to zero, except \e m11 and \e m22 (scaling)
+    which are set to 1.
+
+    \sa isIdentity()
+*/
+
+void TQWMatrix::reset()
+{
+    _m11 = _m22 = 1.0;
+    _m12 = _m21 = _dx = _dy = 0.0;
+}
+
+/*!
+    Returns TRUE if the matrix is the identity matrix; otherwise returns FALSE.
+
+    \sa reset()
+*/
+bool TQWMatrix::isIdentity() const
+{
+    return _m11 == 1.0 && _m22 == 1.0 && _m12 == 0.0 && _m21 == 0.0
+	&& _dx == 0.0 && _dy == 0.0;
+}
+
+/*!
+    Moves the coordinate system \a dx along the X-axis and \a dy along
+    the Y-axis.
+
+    Returns a reference to the matrix.
+
+    \sa scale(), shear(), rotate()
+*/
+
+TQWMatrix &TQWMatrix::translate( double dx, double dy )
+{
+    _dx += dx*_m11 + dy*_m21;
+    _dy += dy*_m22 + dx*_m12;
+    return *this;
+}
+
+/*!
+    Scales the coordinate system unit by \a sx horizontally and \a sy
+    vertically.
+
+    Returns a reference to the matrix.
+
+    \sa translate(), shear(), rotate()
+*/
+
+TQWMatrix &TQWMatrix::scale( double sx, double sy )
+{
+    _m11 *= sx;
+    _m12 *= sx;
+    _m21 *= sy;
+    _m22 *= sy;
+    return *this;
+}
+
+/*!
+    Shears the coordinate system by \a sh horizontally and \a sv
+    vertically.
+
+    Returns a reference to the matrix.
+
+    \sa translate(), scale(), rotate()
+*/
+
+TQWMatrix &TQWMatrix::shear( double sh, double sv )
+{
+    double tm11 = sv*_m21;
+    double tm12 = sv*_m22;
+    double tm21 = sh*_m11;
+    double tm22 = sh*_m12;
+    _m11 += tm11;
+    _m12 += tm12;
+    _m21 += tm21;
+    _m22 += tm22;
+    return *this;
+}
+
+const double deg2rad = 0.017453292519943295769;	// pi/180
+
+/*!
+    Rotates the coordinate system \a a degrees counterclockwise.
+
+    Returns a reference to the matrix.
+
+    \sa translate(), scale(), shear()
+*/
+
+TQWMatrix &TQWMatrix::rotate( double a )
+{
+    double b = deg2rad*a;			// convert to radians
+#if defined(Q_WS_X11)
+    double sina = qsincos(b,FALSE);		// fast and convenient
+    double cosa = qsincos(b,TRUE);
+#else
+    double sina = sin(b);
+    double cosa = cos(b);
+#endif
+    double tm11 = cosa*_m11 + sina*_m21;
+    double tm12 = cosa*_m12 + sina*_m22;
+    double tm21 = -sina*_m11 + cosa*_m21;
+    double tm22 = -sina*_m12 + cosa*_m22;
+    _m11 = tm11; _m12 = tm12;
+    _m21 = tm21; _m22 = tm22;
+    return *this;
+}
+
+/*!
+    \fn bool TQWMatrix::isInvertible() const
+
+    Returns TRUE if the matrix is invertible; otherwise returns FALSE.
+
+    \sa invert()
+*/
+
+/*!
+    \fn double TQWMatrix::det() const
+
+    Returns the matrix's determinant.
+*/
+
+
+/*!
+    Returns the inverted matrix.
+
+    If the matrix is singular (not invertible), the identity matrix is
+    returned.
+
+    If \a invertible is not 0: the value of \a *invertible is set
+    to TRUE if the matrix is invertible; otherwise \a *invertible is
+    set to FALSE.
+
+    \sa isInvertible()
+*/
+
+TQWMatrix TQWMatrix::invert( bool *invertible ) const
+{
+    double determinant = det();
+    if ( determinant == 0.0 ) {
+	if ( invertible )
+	    *invertible = FALSE;		// singular matrix
+	TQWMatrix defaultMatrix;
+	return defaultMatrix;
+    }
+    else {					// invertible matrix
+	if ( invertible )
+	    *invertible = TRUE;
+	double dinv = 1.0/determinant;
+	TQWMatrix imatrix( (_m22*dinv),	(-_m12*dinv),
+			  (-_m21*dinv), ( _m11*dinv),
+			  ((_m21*_dy - _m22*_dx)*dinv),
+			  ((_m12*_dx - _m11*_dy)*dinv) );
+	return imatrix;
+    }
+}
+
+
+/*!
+    Returns TRUE if this matrix is equal to \a m; otherwise returns FALSE.
+*/
+
+bool TQWMatrix::operator==( const TQWMatrix &m ) const
+{
+    return _m11 == m._m11 &&
+	   _m12 == m._m12 &&
+	   _m21 == m._m21 &&
+	   _m22 == m._m22 &&
+	   _dx == m._dx &&
+	   _dy == m._dy;
+}
+
+/*!
+    Returns TRUE if this matrix is not equal to \a m; otherwise returns FALSE.
+*/
+
+bool TQWMatrix::operator!=( const TQWMatrix &m ) const
+{
+    return _m11 != m._m11 ||
+	   _m12 != m._m12 ||
+	   _m21 != m._m21 ||
+	   _m22 != m._m22 ||
+	   _dx != m._dx ||
+	   _dy != m._dy;
+}
+
+/*!
+    Returns the result of multiplying this matrix by matrix \a m.
+*/
+
+TQWMatrix &TQWMatrix::operator*=( const TQWMatrix &m )
+{
+    double tm11 = _m11*m._m11 + _m12*m._m21;
+    double tm12 = _m11*m._m12 + _m12*m._m22;
+    double tm21 = _m21*m._m11 + _m22*m._m21;
+    double tm22 = _m21*m._m12 + _m22*m._m22;
+
+    double tdx  = _dx*m._m11  + _dy*m._m21 + m._dx;
+    double tdy =  _dx*m._m12  + _dy*m._m22 + m._dy;
+
+    _m11 = tm11; _m12 = tm12;
+    _m21 = tm21; _m22 = tm22;
+    _dx = tdx; _dy = tdy;
+    return *this;
+}
+
+/*!
+    \overload
+    \relates TQWMatrix
+    Returns the product of \a m1 * \a m2.
+
+    Note that matrix multiplication is not commutative, i.e. a*b !=
+    b*a.
+*/
+
+TQWMatrix operator*( const TQWMatrix &m1, const TQWMatrix &m2 )
+{
+    TQWMatrix result = m1;
+    result *= m2;
+    return result;
+}
+
+/*****************************************************************************
+  TQWMatrix stream functions
+ *****************************************************************************/
+#ifndef QT_NO_DATASTREAM
+/*!
+    \relates TQWMatrix
+
+    Writes the matrix \a m to the stream \a s and returns a reference
+    to the stream.
+
+    \sa \link datastreamformat.html Format of the TQDataStream operators \endlink
+*/
+
+TQDataStream &operator<<( TQDataStream &s, const TQWMatrix &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 << m.m11() << m.m12() << m.m21() << m.m22()
+	  << m.dx() << m.dy();
+    return s;
+}
+
+/*!
+    \relates TQWMatrix
+
+    Reads the matrix \a m from the stream \a s and returns a reference
+    to the stream.
+
+    \sa \link datastreamformat.html Format of the TQDataStream operators \endlink
+*/
+
+TQDataStream &operator>>( TQDataStream &s, TQWMatrix &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
+
+#endif // QT_NO_WMATRIX
+