QWMatrix(3qt)

NAME
QWMatrix - 2D transformations of a coordinate system

SYNOPSIS

#include <qwmatrix.h>

  Public Members
QWMatrix ()
QWMatrix ( float m11, float m12, float m21, float m22, float dx, float dy )
void setMatrix ( float m11, float m12, float m21, float m22, float dx, float dy )
float m11 () const
float m12 () const
float m21 () const
float m22 () const
float dx () const
float dy () const
void map ( int x, int y, int * tx, int * ty ) const
void map ( float x, float y, float * tx, float * ty ) const
QPoint map ( const QPoint & ) const
QRect map ( const QRect & ) const
QPointArray map ( const QPointArray & ) const
void reset ()
QWMatrix& translate ( float dx, float dy )
QWMatrix& scale ( float sx, float sy )
QWMatrix& shear ( float sh, float sv )
QWMatrix& rotate ( float a )
QWMatrix invert ( bool * = 0 ) const
bool operator== ( const QWMatrix & ) const
bool operator!= ( const QWMatrix & ) const
QWMatrix& operator*= ( const QWMatrix & )

RELATED FUNCTION DOCUMENTATION
(Note that these are not member functions.)
QWMatrix operator* (const QWMatrix & m1, const QWMatrix & m2)
QDataStream & operator<< (QDataStream & s, const QWMatrix & m)
QDataStream & operator>> (QDataStream & s, QWMatrix & m)

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:

    float a    = pi/180 * 25;                   // convert 25 to radians
    float sina = sin(a);
    float 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 desktop/desktop.cpp drawdemo/drawdemo.cpp movies/main.cpp xform/xform.cpp aclock/aclock.cpp qmag/qmag.cpp showimg/showimg.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 ( float m11, float m12, float m21, float m22, float dx, float dy )
Constructs a matrix with the specified elements.

float QWMatrix::dx () const
Returns the horizontal translation.

float 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.

float QWMatrix::m11 () const
Returns the X scaling factor.

float QWMatrix::m12 () const
Returns the vertical shearing factor.

float QWMatrix::m21 () const
Returns the horizontal shearing factor.

float 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 tranformed rectangle r.

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

void QWMatrix::map ( float x, float y, float * tx, float * ty ) const
Transforms (x,y) to (*tx,*ty), using the formulae:

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

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: xform/xform.cpp

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 ( float a )
Rotates the coordinate system a degrees counterclockwise.

Returns a reference to the matrix.

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

Examples: desktop/desktop.cpp drawdemo/drawdemo.cpp xform/xform.cpp aclock/aclock.cpp

QWMatrix & QWMatrix::scale ( float sx, float 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 movies/main.cpp xform/xform.cpp aclock/aclock.cpp showimg/showimg.cpp

void QWMatrix::setMatrix ( float m11, float m12, float m21, float m22, float dx, float dy )
Sets the matrix elements to the specified values.

QWMatrix & QWMatrix::shear ( float sh, float 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 xform/xform.cpp

QWMatrix & QWMatrix::translate ( float dx, float 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: drawdemo/drawdemo.cpp xform/xform.cpp aclock/aclock.cpp

RELATED FUNCTION DOCUMENTATION

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.

QDataStream & operator<< (QDataStream & s, const QWMatrix & m)
Writes a matrix to the stream and returns a reference to the stream.

Serialization format: m11, m12, m21, m22, dx and dy are serialized as float in the listed order.

QDataStream & operator>> (QDataStream & s, QWMatrix & m)
Reads a matrix from the stream and returns a reference to the stream.

SEE ALSO
http://www.troll.no/qt/qwmatrix.html

COPYRIGHT
Copyright 1992-1997 Troll Tech AS. See the LICENSE file included in the distribution for a complete license statement.

AUTHOR
Generated automatically from the source code.