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

#include <qwmatrix.h>

Tipos públicos
enum	TransformationMode { Points, Areas, Points, Areas }
enum	TransformationMode { Points, Areas, Points, Areas }
Métodos públicos
	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 &) const
QPoint	map (const QPoint &p) const
QRect	map (const QRect &r) const
QPointArray	map (const QPointArray &a) const
QRegion	map (const QRegion &r) const
QRegion	mapToRegion (const QRect &r) const
QPointArray	mapToPolygon (const QRect &r) const
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
double	det () const
QWMatrix	invert (bool *=0) const
bool	operator== (const QWMatrix &) const
bool	operator!= (const QWMatrix &) const
QWMatrix &	operator*= (const QWMatrix &)
QPoint	operator* (const QPoint &) const
QRegion	operator* (const QRect &) const
QRegion	operator* (const QRegion &) const
QPointArray	operator* (const QPointArray &a) const
	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 &) const
QPoint	map (const QPoint &p) const
QRect	map (const QRect &r) const
QPointArray	map (const QPointArray &a) const
QRegion	map (const QRegion &r) const
QRegion	mapToRegion (const QRect &r) const
QPointArray	mapToPolygon (const QRect &r) const
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
double	det () const
QWMatrix	invert (bool *=0) const
bool	operator== (const QWMatrix &) const
bool	operator!= (const QWMatrix &) const
QWMatrix &	operator*= (const QWMatrix &)
QPoint	operator* (const QPoint &) const
QRegion	operator* (const QRect &) const
QRegion	operator* (const QRegion &) const
QPointArray	operator* (const QPointArray &a) const
Métodos públicos estáticos
static void	setTransformationMode (QWMatrix::TransformationMode m)
static TransformationMode	transformationMode ()
static void	setTransformationMode (QWMatrix::TransformationMode m)
static TransformationMode	transformationMode ()
Funciones relacionadas
(Observar que estas no son funciones miembro.)
QWMatrix	operator* (const QWMatrix &m1, const QWMatrix &m2)
QDataStream &	operator<< (QDataStream &s, const QWMatrix &m)
QDataStream &	operator>> (QDataStream &s, QWMatrix &m)

Descripción detallada

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 the 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 3x3 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 also 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(1, 0, 0, 1, 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.

Ver también:: QPainter::setWorldMatrix(), QPixmap::xForm()

Documentación de las enumeraciones miembro de la clase

enum QWMatrix::TransformationMode

transformation matrix

QWMatrix 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.

Points transformations are applied to the shape's points. Areas transformations are applied (e.g. to the width and height) so that the area is transformed.

Example:

Suppose we have a rectangle, {QRect( 10, 20, 30, 40 )} and a transformation matrix {QWMatrix( 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, {matrix * ( region1 | region2 )} is not equal to {matrix * region1 | matrix * region2}. Under Area mode, {matrix * (pointarray[i])} is not neccesarily equal to {(matrix * pointarry)[i]}.

xform.png Comparison of Points and Areas TransformationModes

Valores de enumeraciones:

Points
Areas
Points
Areas

enum QWMatrix::TransformationMode

Valores de enumeraciones:

Points
Areas
Points
Areas

Documentación del constructor y destructor

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.

QWMatrix::QWMatrix ( )

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

Documentación de las funciones miembro

double QWMatrix::det ( ) const [inline]

Returns the matrix's determinant.

double QWMatrix::det ( ) const [inline]

double QWMatrix::dx ( ) const [inline]

Returns the horizontal translation.

double QWMatrix::dy ( ) const [inline]

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 0: the value of *invertible is set to TRUE if the matrix is invertible; otherwise *invertible is set to FALSE.

Ver también:: isInvertible()

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

bool QWMatrix::isIdentity ( ) const

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

Ver también:: reset()

bool QWMatrix::isIdentity ( ) const

bool QWMatrix::isInvertible ( ) const [inline]

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

Ver también:: invert()

bool QWMatrix::isInvertible ( ) const [inline]

double QWMatrix::m11 ( ) const [inline]

Returns the X scaling factor.

double QWMatrix::m12 ( ) const [inline]

Returns the vertical shearing factor.

double QWMatrix::m21 ( ) const [inline]

Returns the horizontal shearing factor.

double QWMatrix::m21 ( ) const [inline]

double QWMatrix::m22 ( ) const [inline]

Returns the Y scaling factor.

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

Esta es una función miembro sobrecargada que se suministra por conveniencia. Difiere de la anterior función solamente en los argumentos que acepta. Transforms ( x, y ) to ( *tx, *ty ) using the following 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)

QPointArray QWMatrix::map ( const QPointArray & a ) const [inline]

QRect QWMatrix::map ( const QRect & r ) const [inline]

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

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

QPoint QWMatrix::map ( const QPoint & p ) const [inline]

Esta es una función miembro sobrecargada que se suministra por conveniencia. Difiere de la anterior función solamente en los argumentos que acepta. 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)

QRect QWMatrix::map ( const QRect & r ) const [inline]

Please use QWMatrix::mapRect() instead.

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

QRegion QWMatrix::map ( const QRegion & r ) const [inline]

QPointArray QWMatrix::map ( const QPointArray & a ) const [inline]

Esta es una función miembro sobrecargada que se suministra por conveniencia. Difiere de la anterior función solamente en los argumentos que acepta. Returns the point array a transformed by calling map for each point.

QRegion QWMatrix::map ( const QRegion & r ) const [inline]

Esta es una función miembro sobrecargada que se suministra por conveniencia. Difiere de la anterior función solamente en los argumentos que acepta. Transforms the region r.

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

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*().

Ver también:: operator*()

QRect QWMatrix::mapRect ( const QRect & ) const

QPointArray QWMatrix::mapToPolygon ( const QRect & rect ) const

Returns the transformed rectangle rect as a polygon.

Polygons and rectangles behave slightly differently when transformed (due to integer rounding), so {matrix.map( QPointArray( rect ) )} is not always the same as {matrix.mapToPolygon( rect )}.

QPointArray QWMatrix::mapToPolygon ( const QRect & r ) const

QRegion QWMatrix::mapToRegion ( const QRect & r ) const [inline]

QRegion QWMatrix::mapToRegion ( const QRect & rect ) const [inline]

Returns the transformed rectangle 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.

Ver también:: QWMatrix::mapRect()

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

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

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

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

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

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

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

QRegion QWMatrix::operator* ( const QRect & rect ) const

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

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

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

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

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

Returns the result of multiplying this matrix by matrix m.

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

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

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

void QWMatrix::reset ( void )

Resets the matrix to an identity matrix.

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

Ver también:: isIdentity()

void QWMatrix::reset ( )

QWMatrix& QWMatrix::rotate ( double a )

QWMatrix & QWMatrix::rotate ( double a )

Rotates the coordinate system a degrees counterclockwise.

Returns a reference to the matrix.

Ver también:: translate(), scale(), shear()

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

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

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

Returns a reference to the matrix.

Ver también:: translate(), shear(), rotate()

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.

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

void QWMatrix::setTransformationMode ( QWMatrix::TransformationMode m ) [static]

Sets the transformation mode that QWMatrix and painter transformations use to m.

Ver también:: QWMatrix::TransformationMode

static void QWMatrix::setTransformationMode ( QWMatrix::TransformationMode m ) [static]

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

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

Shears the coordinate system by sh horizontally and sv vertically.

Returns a reference to the matrix.

Ver también:: translate(), scale(), rotate()

static TransformationMode QWMatrix::transformationMode ( ) [static]

QWMatrix::TransformationMode QWMatrix::transformationMode ( ) [static]

Returns the current transformation mode.

Ver también:: QWMatrix::TransformationMode

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

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.

Ver también:: scale(), shear(), rotate()

Documentación de las funciones relacionadas y clases amigas

QWMatrix operator*	(	const QWMatrix &	m1,
		const QWMatrix &	m2
	)		`[related]`

Esta es una función miembro sobrecargada que se suministra por conveniencia. Difiere de la anterior función solamente en los argumentos que acepta. 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
	)		`[related]`

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

Ver también:: Format of the QDataStream operators

QDataStream & operator>>	(	QDataStream &	s,
		QWMatrix &	m
	)		`[related]`

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

Ver también:: Format of the QDataStream operators

La documentación para esta clase fue generada a partir de los siguientes ficheros:

src/qt/include/qwmatrix.h
src/qt/src/kernel/qwmatrix.h
src/qt/src/kernel/qwmatrix.cpp

Tipos públicos

Métodos públicos

Métodos públicos estáticos

Funciones relacionadas

Descripción detallada

Documentación de las enumeraciones miembro de la clase

Documentación del constructor y destructor

Documentación de las funciones miembro

Documentación de las funciones relacionadas y clases amigas