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# QWMatrix Class Reference

The QWMatrix class specifies 2D transformations of a coordinate system. More...

`#include <qwmatrix.h>`

List of all member functions.

## Public Members

- QWMatrix ()
- QWMatrix ( double m11, double m12, double m21, double m22, double dx, double dy )
- void setMatrix ( double m11, double m12, double m21, double m22, double dx, double dy )
- double m11 () const
- double m12 () const
- double m21 () const
- double m22 () const
- double dx () const
- double dy () const
- void map ( int x, int y, int * tx, int * ty ) const
- void map ( double x, double y, double * tx, double * ty ) const
- QRect mapRect ( const QRect & rect ) const
- QPoint map ( const QPoint & p ) const (obsolete)
- QRect map ( const QRect & r ) const (obsolete)
- QPointArray map ( const QPointArray & a ) const (obsolete)
- void reset ()
- bool isIdentity () const
- QWMatrix & translate ( double dx, double dy )
- QWMatrix & scale ( double sx, double sy )
- QWMatrix & shear ( double sh, double sv )
- QWMatrix & rotate ( double a )
- bool isInvertible () const
- QWMatrix invert ( bool * invertible = 0 ) const
- bool operator== ( const QWMatrix & m ) const
- bool operator!= ( const QWMatrix & m ) const
- QWMatrix & operator*= ( const QWMatrix & m )
- QPoint operator* ( const QPoint & p ) const
- QRegion operator* ( const QRect & r ) const
- QRegion operator* ( const QRegion & r ) const
- QPointArray operator* ( const QPointArray & a ) const

## Related Functions

- QWMatrix operator* ( const QWMatrix & m1, const QWMatrix & m2 )
- QDataStream & operator<< ( QDataStream & s, const QWMatrix & m )
- QDataStream & operator>> ( QDataStream & s, QWMatrix & m )

## Detailed Description

The QWMatrix class specifies 2D transformations of a coordinate system.

The standard coordinate system of a paint device has the origin located at the top-left position. X values increase to the right; Y values increase downward.

This coordinate system is default for the QPainter, which renders graphics in a paint device. A user-defined coordinate system can be specified by setting a QWMatrix for the painter.

Example:

        MyWidget::paintEvent( QPaintEvent * )
        {
          QPainter p;                       // our painter
          QWMatrix 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
        }

A matrix specifies how to translate, scale, shear or rotate the graphics; the actual transformation is performed by the drawing routines in QPainter and by QPixmap::xForm().

The QWMatrix class contains a 3*3 matrix of the form:

        m11  m12  0
        m21  m22  0
        dx   dy   1

A matrix transforms a point in the plane to another point:

        x' = m11*x + m21*y + dx
        y' = m22*y + m12*x + dy

The point (x, y) is the original point, and (x', y') is the transformed point. (x', y') can be transformed back to (x, y) by performing the same operation on the inverted matrix.

The elements dx and dy specify horizontal and vertical translation. The elements m11 and m22 specify horizontal and vertical scaling. The elements m12 and m21 specify horizontal and vertical shearing.

The identity matrix has m11 and m22 set to 1; all others are set to 0. This matrix maps a point to itself.

Translation is the simplest transformation. Setting dx and dy will move the coordinate system dx units along the X axis and dy units along the Y axis.

Scaling can be done by setting m11 and m22. For example, setting m11 to 2 and m22 to 1.5 will double the height and increase the width by 50%.

Shearing is controlled by m12 and 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 QWMatrix has a function that sets rotation directly.

QWMatrix lets you combine transformations like this:

        QWMatrix 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

Here's the same example using basic matrix operations:

        double a    = pi/180 * 25;         // convert 25 to radians
        double sina = sin(a);
        double cosa = cos(a);
        QWMatrix m1(0, 0, 0, 0, 10, -20);  // translation matrix
        QWMatrix m2( cosa, sina,           // rotation matrix
                     -sina, cosa, 0, 0 );
        QWMatrix m3(1.2, 0, 0, 0.7, 0, 0); // scaling matrix
        QWMatrix m;
        m = m3 * m2 * m1;                  // combine all transformations

QPainter has functions to translate, scale, shear and rotate the coordinate system without using a QWMatrix. Although these functions are very convenient, it can be more efficient to build a QWMatrix and call QPainter::setWorldMatrix() if you want to perform more than a single transform operation.

See also QPainter::setWorldMatrix(), QPixmap::xForm(), Graphics Classes and Image Processing Classes.

## Member Function Documentation

### QWMatrix::QWMatrix ()

Constructs an identity matrix. All elements are set to zero except m11 and m22 (scaling), which are set to 1.

### QWMatrix::QWMatrix ( double m11, double m12, double m21, double m22, double dx, double dy )

Constructs a matrix with the elements, m11, m12, m21, m22, dx and dy.

### double QWMatrix::dx () const

Returns the horizontal translation.

### double QWMatrix::dy () const

Returns the vertical translation.

### QWMatrix QWMatrix::invert ( bool * invertible = 0 ) const

Returns the inverted matrix.

If the matrix is singular (not invertible), the identity matrix is returned.

If invertible is not null, the value of *invertible is set to TRUE if the matrix is invertible or to FALSE if the matrix is not invertible.

See also isInvertible().

Example: t14/cannon.cpp.

### bool QWMatrix::isIdentity () const

Returns TRUE if the matrix is the identity matrix; otherwise returns FALSE.

See also reset().

### bool QWMatrix::isInvertible () const

Returns TRUE if the matrix is invertible; otherwise returns FALSE.

See also invert().

### double QWMatrix::m11 () const

Returns the X scaling factor.

### double QWMatrix::m12 () const

Returns the vertical shearing factor.

### double QWMatrix::m21 () const

Returns the horizontal shearing factor.

### double QWMatrix::m22 () const

Returns the Y scaling factor.

### void QWMatrix::map ( int x, int y, int * tx, int * ty ) const

Transforms ( x, y ) to ( *tx, *ty ) using the formulae:

        *tx = m11*x + m21*y + dx  (rounded to the nearest integer)
        *ty = m22*y + m12*x + dy  (rounded to the nearest integer)

Examples: t14/cannon.cpp and xform/xform.cpp.

### void QWMatrix::map ( double x, double y, double * tx, double * ty ) const

This is an overloaded member function, provided for convenience. It behaves essentially like the above function.

Transforms ( x, y ) to ( *tx, *ty ) using the following formulae:

        *tx = m11*x + m21*y + dx
        *ty = m22*y + m12*x + dy

### QPoint QWMatrix::map ( const QPoint & p ) const

This function is obsolete. It is provided to keep old source working. We strongly advise against using it in new code.

Does the same as operator *( const QPoint &)

### QRect QWMatrix::map ( const QRect & r ) const

This function is obsolete. It is provided to keep old source working. We strongly advise against using it in new code.

Please use QWMatrix::mapRect() instead.

Note that this method does return the bounding rectangle of the r, when shearing or rotations are used.

### QPointArray QWMatrix::map ( const QPointArray & a ) const

This function is obsolete. It is provided to keep old source working. We strongly advise against using it in new code.

Does the same as operator *( const QPointArray &)

### QRect QWMatrix::mapRect ( const QRect & rect ) const

Returns the transformed rectangle rect.

The bounding rectangle is returned if rotation or shearing has been specified.

If you need to know the exact region rect maps to use operator*().

See also operator*().

### bool QWMatrix::operator!= ( const QWMatrix & m ) const

Returns TRUE if this matrix is not equal to m; otherwise returns FALSE.

### QPoint QWMatrix::operator* ( const QPoint & p ) const

Transforms p to using the formulae:

        retx = m11*px + m21*py + dx  (rounded to the nearest integer)
        rety = m22*py + m12*px + dy  (rounded to the nearest integer)

### QRegion QWMatrix::operator* ( const QRect & r ) const

This is an overloaded member function, provided for convenience. It behaves essentially like the above function.

Transforms the rectangle r.

Rotation and shearing a rectangle results in a more general region, which is returned here.

Calling this method can be rather 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.

See also QWMatrix::mapRect().

### QRegion QWMatrix::operator* ( const QRegion & r ) const

This is an overloaded member function, provided for convenience. It behaves essentially like the above function.

Transforms the region r.

Calling this method can be rather expensive, if rotations or shearing are used.

### QPointArray QWMatrix::operator* ( const QPointArray & a ) const

This is an overloaded member function, provided for convenience. It behaves essentially like the above function.

Returns the point array a transformed by calling map for each point.

### QWMatrix & QWMatrix::operator*= ( const QWMatrix & m )

Returns the result of multiplying this matrix with matrix m.

### bool QWMatrix::operator== ( const QWMatrix & m ) const

Returns TRUE if this matrix is equal to m; otherwise returns FALSE.

### void QWMatrix::reset ()

Resets the matrix to an identity matrix.

All elements are set to zero, except m11 and m22 (scaling) that are set to 1.

See also isIdentity().

### QWMatrix & QWMatrix::rotate ( double a )

Rotates the coordinate system a degrees counterclockwise.

Returns a reference to the matrix.

See also translate(), scale() and shear().

Examples: canvas/canvas.cpp, desktop/desktop.cpp, drawdemo/drawdemo.cpp, t14/cannon.cpp and xform/xform.cpp.

### QWMatrix & QWMatrix::scale ( double sx, double sy )

Scales the coordinate system unit by sx horizontally and sy vertically.

Returns a reference to the matrix.

See also translate(), shear() and rotate().

Examples: canvas/canvas.cpp, fileiconview/qfileiconview.cpp, movies/main.cpp, qmag/qmag.cpp, qtimage/qtimage.cpp, showimg/showimg.cpp and xform/xform.cpp.

### void QWMatrix::setMatrix ( double m11, double m12, double m21, double m22, double dx, double dy )

Sets the matrix elements to the specified values, m11, m12, m21, m22, dx and dy.

### QWMatrix & QWMatrix::shear ( double sh, double sv )

Shears the coordinate system by sh horizontally and sv vertically.

Returns a reference to the matrix.

See also translate(), scale() and rotate().

Examples: drawdemo/drawdemo.cpp and xform/xform.cpp.

### QWMatrix & QWMatrix::translate ( double dx, double dy )

Moves the coordinate system dx along the X-axis and dy along the Y-axis.

Returns a reference to the matrix.

See also scale(), shear() and rotate().

Examples: canvas/canvas.cpp, drawdemo/drawdemo.cpp, t14/cannon.cpp and xform/xform.cpp.

## Related Functions

### QWMatrix operator* ( const QWMatrix & m1, const QWMatrix & m2 )

This is an overloaded member function, provided for convenience. It behaves essentially like the above function.

Returns the product of m1 * m2.

Note that matrix multiplication is not commutative, i.e. a*b != b*a.

### QDataStream & operator<< ( QDataStream & s, const QWMatrix & m )

Writes the matrix m to the stream s and returns a reference to the stream.

See also Format of the QDataStream operators.

### QDataStream & operator>> ( QDataStream & s, QWMatrix & m )

Reads the matrix m from the stream s and returns a reference to the stream.

See also Format of the QDataStream operators.

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