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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
- QPoint map ( const QPoint & ) const
- QRect map ( const QRect & ) const
- QPointArray map ( const QPointArray & ) const
- void reset ()
- QWMatrix& translate ( double dx, double dy )
- QWMatrix& scale ( double sx, double sy )
- QWMatrix& shear ( double sh, double sv )
- QWMatrix& rotate ( double a )
- QWMatrix invert ( bool * = 0 ) const
- bool operator== ( const QWMatrix & ) const
- bool operator!= ( const QWMatrix & ) const
- QWMatrix& operator*= ( const QWMatrix & )

## Related Functions

(Note that these are not member functions.)

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

## 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, and Y values increase downwards.

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, and 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 horisontal and vertical translation. The elements m11 and m22 specify horisontal and vertical scaling. The elements m12 and m21 specify horisontal and vertical shearing.

The identity matrix has m11 and m22 set to 1, all others 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

The same example, but 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 that translate, scale, shear and rotate the coordinate system without using a QWMatrix. These functions are very convenient, however, if you want to perform more than a single transform operation, it is more efficient to build a QWMatrix and call QPainter::setWorldMatrix().

See also QPainter::setWorldMatrix() and QPixmap::xForm().

Examples: qtimage/qtimage.cpp xform/xform.cpp drawdemo/drawdemo.cpp qmag/qmag.cpp desktop/desktop.cpp movies/main.cpp

## 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 specified elements.

### 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), then the identity matrix is returned.

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

### 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.

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

Returns the transformed p.

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

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

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

Returns the transformed rectangle r.

If rotation or shearing has been specified, then the bounding rectangle will be returned.

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

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

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

Examples: xform/xform.cpp

### 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)

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

Returns TRUE if this matrix is not equal to m.

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

Returns the result of multiplying this matrix with m.

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

Returns TRUE if this matrix is equal to m.

### 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.

### 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: xform/xform.cpp drawdemo/drawdemo.cpp desktop/desktop.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: qtimage/qtimage.cpp xform/xform.cpp movies/main.cpp

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

Sets the matrix elements to the specified values.

### 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: xform/xform.cpp drawdemo/drawdemo.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: xform/xform.cpp drawdemo/drawdemo.cpp

## Related Functions

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

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

See also Format of the QDataStream operators

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

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

See also Format of the QDataStream operators

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

Returns the product m1 * m2.

Remember that matrix multiplication is not commutative, thus a*b != b*a.

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