com.trolltech.qt.gui
Class QMatrix

java.lang.Object
  extended by com.trolltech.qt.internal.QSignalEmitterInternal
      extended by com.trolltech.qt.QSignalEmitter
          extended by com.trolltech.qt.QtJambiObject
              extended by com.trolltech.qt.gui.QMatrix
All Implemented Interfaces:
QtJambiInterface, java.lang.Cloneable

public class QMatrix
extends QtJambiObject
implements java.lang.Cloneable

The QMatrix class specifies 2D transformations of a coordinate system. A matrix specifies how to translate, scale, shear or rotate the coordinate system, and is typically used when rendering graphics.

A QMatrix object can be built using the setMatrix(), scale(), rotate(), translate() and shear() functions. Alternatively, it can be built by applying basic matrix operations. The matrix can also be defined when constructed, and it can be reset to the identity matrix (the default) using the reset() function.

The QMatrix class supports mapping of graphic primitives: A given point, line, polygon, region, or painter path can be mapped to the coordinate system defined by this matrix using the map() function. In case of a rectangle, its coordinates can be transformed using the mapRect() function. A rectangle can also be transformed into a polygon (mapped to the coordinate system defined by this matrix), using the mapToPolygon() function.

QMatrix provides the isIdentity() function which returns true if the matrix is the identity matrix, and the isInvertible() function which returns true if the matrix is non-singular (i.e. AB = BA = I). The inverted() function returns an inverted copy of this matrix if it is invertible (otherwise it returns the identity matrix). In addition, QMatrix provides the det() function returning the matrix's determinant.

Finally, the QMatrix class supports matrix multiplication, and objects of the class can be streamed as well as compared.

Rendering Graphics

When rendering graphics, the matrix defines the transformations but the actual transformation is performed by the drawing routines in
QPainter.

By default, QPainter operates on the associated device's own coordinate system. The standard coordinate system of a QPaintDevice has its origin located at the top-left position. The x values increase to the right; y values increase downward. For a complete description, see the coordinate system documentation.

QPainter has functions to translate, scale, shear and rotate the coordinate system without using a QMatrix. For example:



    protected void paintEvent(QPaintEvent event)
    {
        QPainter painter = new QPainter(this);
        painter.setPen(new QPen(QColor.blue, 1, Qt.PenStyle.DashLine));
        painter.drawRect(0, 0, 100, 100);

        painter.rotate(45);

        painter.setFont(new QFont("Helvetica", 24));
        painter.setPen(new QPen(QColor.black, 1));
        painter.drawText(20, 10, "QMatrix");
    }
    
Although these functions are very convenient, it can be more efficient to build a QMatrix and call QPainter::setMatrix() if you want to perform more than a single transform operation. For example:


    protected void paintEvent(QPaintEvent event)
    {
        QPainter painter = new QPainter(this);
        painter.setPen(new QPen(QColor.blue, 1,
                                Qt.PenStyle.DashLine));
        painter.drawRect(0, 0, 100, 100);

        QMatrix matrix = new QMatrix();
        matrix.translate(50, 50);
        matrix.rotate(45);
        matrix.scale(0.5, 1.0);
        painter.setWorldMatrix(matrix);

        painter.setFont(new QFont("Helvetica", 24));
        painter.setPen(new QPen(QColor.black, 1));
        painter.drawText(20, 10, "QMatrix");
    }
    

Basic Matrix Operations



A QMatrix object contains a 3 x 3 matrix. The dx and dy elements specify horizontal and vertical translation. The m11 and m22 elements specify horizontal and vertical scaling. And finally, the m21 and m12 elements specify horizontal and vertical shearing.

QMatrix transforms a point in the plane to another point using the following formulas:

        x' = m11 + m21 + dx
        y' = m22 + m12 + 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 various matrix elements can be set when constructing the matrix, or by using the setMatrix() function later on. They can also be manipulated using the translate(), rotate(), scale() and shear() convenience functions, The currently set values can be retrieved using the m11(), m12(), m21(), m22(), dx() and dy() functions.

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%. The identity matrix has m11 and m22 set to 1 (all others are set to 0) mapping a point to itself. 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.

Here's the combined transformations example using basic matrix operations:



    protected void paintEvent(QPaintEvent event)
    {
        double pi = 3.14;

        double a    = pi/180 * 45.0;
        double sina = Math.sin(a);
        double cosa = Math.cos(a);

        QMatrix translationMatrix = new QMatrix(1, 0, 0, 1, 50.0, 50.0);
        QMatrix rotationMatrix = new QMatrix(cosa, sina, -sina, cosa, 0, 0);
        QMatrix scalingMatrix = new QMatrix(0.5, 0, 0, 1.0, 0, 0);

        QMatrix matrix = new QMatrix();
        matrix =  scalingMatrix.multiply(rotationMatrix.multiply(translationMatrix));

        QPainter painter = new QPainter(this);
        painter.setPen(new QPen(QColor.blue, 1, Qt.PenStyle.DashLine));
        painter.drawRect(0, 0, 100, 100);

        painter.setWorldMatrix(matrix);

        painter.setFont(new QFont("Helvetica", 24));
        painter.setPen(new QPen(QColor.black, 1));
        painter.drawText(20, 10, "QMatrix");
    }
    

See also:
QPainter, The Coordinate System, Affine Transformations Demo, and Transformations Example.


Nested Class Summary
 
Nested classes/interfaces inherited from class com.trolltech.qt.QSignalEmitter
QSignalEmitter.AbstractSignal, QSignalEmitter.PrivateSignal0, QSignalEmitter.PrivateSignal1, QSignalEmitter.PrivateSignal2, QSignalEmitter.PrivateSignal3, QSignalEmitter.PrivateSignal4, QSignalEmitter.PrivateSignal5, QSignalEmitter.PrivateSignal6, QSignalEmitter.PrivateSignal7, QSignalEmitter.PrivateSignal8, QSignalEmitter.PrivateSignal9, QSignalEmitter.Signal0, QSignalEmitter.Signal1, QSignalEmitter.Signal2, QSignalEmitter.Signal3, QSignalEmitter.Signal4, QSignalEmitter.Signal5, QSignalEmitter.Signal6, QSignalEmitter.Signal7, QSignalEmitter.Signal8, QSignalEmitter.Signal9
 
Nested classes/interfaces inherited from class com.trolltech.qt.internal.QSignalEmitterInternal
com.trolltech.qt.internal.QSignalEmitterInternal.AbstractSignalInternal
 
Field Summary
 
Fields inherited from class com.trolltech.qt.internal.QSignalEmitterInternal
currentSender
 
Constructor Summary
QMatrix()
          Constructs an identity matrix.
QMatrix(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.
QMatrix(QMatrix matrix)
          Constructs a matrix that is a copy of the given matrix.
 
Method Summary
 QMatrix clone()
           
 double det()
          Returns the matrix's determinant.
 double dx()
          Returns the horizontal translation factor.
 double dy()
          Returns the vertical translation factor.
 QMatrix inverted()
          Returns an inverted copy of this matrix.
 boolean isIdentity()
          Returns true if the matrix is the identity matrix, otherwise returns false.
 boolean isInvertible()
          Returns true if the matrix is invertible, otherwise returns false.
 double m11()
          Returns the horizontal scaling factor.
 double m12()
          Returns the vertical shearing factor.
 double m21()
          Returns the horizontal shearing factor.
 double m22()
          Returns the vertical scaling factor.
 QLine map(QLine l)
          This is an overloaded member function, provided for convenience.
 QLineF map(QLineF l)
          This is an overloaded member function, provided for convenience.
 QPainterPath map(QPainterPath p)
          This is an overloaded member function, provided for convenience.
 QPoint map(QPoint p)
          This is an overloaded member function, provided for convenience.
 QPointF map(QPointF p)
          This is an overloaded member function, provided for convenience.
 QPolygon map(QPolygon a)
          This is an overloaded member function, provided for convenience.
 QPolygonF map(QPolygonF a)
          This is an overloaded member function, provided for convenience.
 QRegion map(QRegion r)
          This is an overloaded member function, provided for convenience.
 QRect mapRect(QRect arg__1)
          This is an overloaded member function, provided for convenience.
 QRectF mapRect(QRectF arg__1)
          Creates and returns a QRectF object that is a copy of the given rectangle, mapped into the coordinate system defined by this matrix.
 QPolygon mapToPolygon(QRect r)
          Creates and returns a QPolygon representation of the given rectangle, mapped into the coordinate system defined by this matrix.
 QMatrix multiplied(QMatrix other)
           
 QMatrix multiply(QMatrix other)
           
 void readFrom(QDataStream arg__1)
          Reads a QMatrix
 void reset()
          Resets the matrix to an identity matrix, i.
 QMatrix rotate(double other)
          Rotates the coordinate system the given other degrees counterclockwise.
 QMatrix scale(double sx, double sy)
          Scales the coordinate system by sx horizontally and sy vertically, and returns a reference to the matrix.
 void 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.
 QMatrix shear(double sh, double sv)
          Shears the coordinate system by sh horizontally and sv vertically, and returns a reference to the matrix.
 java.lang.String toString()
           
 QMatrix translate(double dx, double dy)
          Moves the coordinate system dx along the x axis and dy along the y axis, and returns a reference to the matrix.
 void writeTo(QDataStream arg__1)
          Writes thisQMatrix
 
Methods inherited from class com.trolltech.qt.QtJambiObject
dispose, disposed, equals, finalize, reassignNativeResources, tr, tr, tr
 
Methods inherited from class com.trolltech.qt.QSignalEmitter
blockSignals, disconnect, disconnect, signalsBlocked, signalSender, thread
 
Methods inherited from class com.trolltech.qt.internal.QSignalEmitterInternal
__qt_signalInitialization
 
Methods inherited from class java.lang.Object
getClass, hashCode, notify, notifyAll, wait, wait, wait
 
Methods inherited from interface com.trolltech.qt.QtJambiInterface
disableGarbageCollection, nativeId, nativePointer, reenableGarbageCollection, setJavaOwnership
 

Constructor Detail

QMatrix

public QMatrix()
Constructs an identity matrix.

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

See also:
reset().


QMatrix

public QMatrix(QMatrix matrix)
Constructs a matrix that is a copy of the given matrix.


QMatrix

public QMatrix(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.

See also:
setMatrix().

Method Detail

det

public final double det()
Returns the matrix's determinant.


dx

public final double dx()
Returns the horizontal translation factor.

See also:
translate(), and Basic Matrix Operations.


dy

public final double dy()
Returns the vertical translation factor.

See also:
translate(), and Basic Matrix Operations.


isIdentity

public final boolean isIdentity()
Returns true if the matrix is the identity matrix, otherwise returns false.

See also:
reset().


isInvertible

public final boolean isInvertible()
Returns true if the matrix is invertible, otherwise returns false.

See also:
inverted().


m11

public final double m11()
Returns the horizontal scaling factor.

See also:
scale(), and Basic Matrix Operations.


m12

public final double m12()
Returns the vertical shearing factor.

See also:
shear(), and Basic Matrix Operations.


m21

public final double m21()
Returns the horizontal shearing factor.

See also:
shear(), and Basic Matrix Operations.


m22

public final double m22()
Returns the vertical scaling factor.

See also:
scale(), and Basic Matrix Operations.


map

public final QLine map(QLine l)
This is an overloaded member function, provided for convenience.

Creates and returns a QLine object that is a copy of the given line, mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.


map

public final QLineF map(QLineF l)
This is an overloaded member function, provided for convenience.

Creates and returns a QLineF object that is a copy of the given line, mapped into the coordinate system defined by this matrix.


map

public final QPainterPath map(QPainterPath p)
This is an overloaded member function, provided for convenience.

Creates and returns a QPainterPath object that is a copy of the given path, mapped into the coordinate system defined by this matrix.


map

public final QPoint map(QPoint p)
This is an overloaded member function, provided for convenience.

Creates and returns a QPoint object that is a copy of the given point, mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.


map

public final QPointF map(QPointF p)
This is an overloaded member function, provided for convenience.

Creates and returns a QPointF object that is a copy of the given point, mapped into the coordinate system defined by this matrix.


map

public final QPolygon map(QPolygon a)
This is an overloaded member function, provided for convenience.

Creates and returns a QPolygon object that is a copy of the given polygon, mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.


map

public final QPolygonF map(QPolygonF a)
This is an overloaded member function, provided for convenience.

Creates and returns a QPolygonF object that is a copy of the given polygon, mapped into the coordinate system defined by this matrix.


map

public final QRegion map(QRegion r)
This is an overloaded member function, provided for convenience.

Creates and returns a QRegion object that is a copy of the given region, mapped into the coordinate system defined by this matrix.

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


mapRect

public final QRect mapRect(QRect arg__1)
This is an overloaded member function, provided for convenience.

Creates and returns a QRect object that is a copy of the given rectangle, mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.


mapRect

public final QRectF mapRect(QRectF arg__1)
Creates and returns a QRectF object that is a copy of the given rectangle, mapped into the coordinate system defined by this matrix.

The rectangle's coordinates are transformed using the following formulas:

        x' = m11 + m21 + dx
        y' = m22 + m12 + dy
If rotation or shearing has been specified, this function returns the bounding rectangle. To retrieve the exact region the given rectangle maps to, use the mapToPolygon() function instead.

See also:
mapToPolygon(), and Basic Matrix Operations.


mapToPolygon

public final QPolygon mapToPolygon(QRect r)
Creates and returns a QPolygon representation of the given rectangle, mapped into the coordinate system defined by this matrix.

The rectangle's coordinates are transformed using the following formulas:

        x' = m11 + m21 + dx
        y' = m22 + m12 + dy
Polygons and rectangles behave slightly differently when transformed (due to integer rounding), so matrix.map(QPolygon(rectangle)) is not always the same as matrix.mapToPolygon(rectangle).

See also:
mapRect(), and Basic Matrix Operations.


writeTo

public final void writeTo(QDataStream arg__1)
Writes thisQMatrix


readFrom

public final void readFrom(QDataStream arg__1)
Reads a QMatrix


reset

public final void reset()
Resets the matrix to an identity matrix, i. . all elements are set to zero, except m11 and m22 (specifying the scale) which are set to 1.

See also:
QMatrix(), isIdentity(), and Basic Matrix Operations.


setMatrix

public final void 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.

Note that this function replaces the previous values. QMatrix provide the translate(), rotate(), scale() and shear() convenience functions to manipulate the various matrix elements based on the currently defined coordinate system.

See also:
QMatrix().


rotate

public final QMatrix rotate(double other)
Rotates the coordinate system the given other degrees counterclockwise.

Note that if you apply a QMatrix to a point defined in widget coordinates, the direction of the rotation will be clockwise because the y-axis points downwards.

Returns a reference to the matrix.


scale

public final QMatrix scale(double sx,
                           double sy)
Scales the coordinate system by sx horizontally and sy vertically, and returns a reference to the matrix.


shear

public final QMatrix shear(double sh,
                           double sv)
Shears the coordinate system by sh horizontally and sv vertically, and returns a reference to the matrix.


translate

public final QMatrix translate(double dx,
                               double dy)
Moves the coordinate system dx along the x axis and dy along the y axis, and returns a reference to the matrix.


inverted

public final QMatrix inverted()
Returns an inverted copy of this matrix.

Returns:
The inverse of the matrix.
Throws:
java.lang.IllegalArgumentException - If this matrix is not invertible.

multiply

public final QMatrix multiply(QMatrix other)

multiplied

public final QMatrix multiplied(QMatrix other)

toString

public java.lang.String toString()
Overrides:
toString in class java.lang.Object

clone

public QMatrix clone()
Overrides:
clone in class java.lang.Object