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diff --git a/src/kernel/qwmatrix.cpp b/src/kernel/qwmatrix.cpp new file mode 100644 index 000000000..f787820bf --- /dev/null +++ b/src/kernel/qwmatrix.cpp @@ -0,0 +1,1036 @@ +/**************************************************************************** +** +** 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> 0 </td></tr> + <tr align=center><td>m21</td><td>m22</td><td> 0 </td></tr> + <tr align=center><td>dx</td> <td>dy</td> <td> 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 + |