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com.trolltech.qt.gui
Class QMatrix

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

public class QMatrix
extends QtJambiObject

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:

    void SimpleTransformation::paintEvent(QPaintEvent *)
    {
        QPainter painter(this);
        painter.setPen(QPen(Qt::blue, 1, Qt::DashLine));
        painter.drawRect(0, 0, 100, 100);

        painter.rotate(45);

        painter.setFont(QFont("Helvetica", 24));
        painter.setPen(QPen(Qt::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:

    void CombinedTransformation::paintEvent(QPaintEvent *)
    {
        QPainter painter(this);
        painter.setPen(QPen(Qt::blue, 1, Qt::DashLine));
        painter.drawRect(0, 0, 100, 100);

        QMatrix matrix;
        matrix.translate(50, 50);
        matrix.rotate(45);
        matrix.scale(0.5, 1.0);
        painter.setMatrix(matrix);

        painter.setFont(QFont("Helvetica", 24));
        painter.setPen(QPen(Qt::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*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 various matrix elements can be set when constructing the matrix, or by using the setMatrix function later on. They 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:

    void BasicOperations::paintEvent(QPaintEvent *)
    {
        double pi = 3.14;

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

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

        QMatrix matrix;
        matrix =  scalingMatrix * rotationMatrix * translationMatrix;

        QPainter painter(this);
        painter.setPen(QPen(Qt::blue, 1, Qt::DashLine));
        painter.drawRect(0, 0, 100, 100);

        painter.setMatrix(matrix);

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

See Also:
QPainter, The Coordinate System, Transformations Demo, Example

Nested Class Summary
 
Nested classes/interfaces inherited from class com.trolltech.qt.QSignalEmitter
QSignalEmitter.AbstractSignal, QSignalEmitter.Signal0, QSignalEmitter.Signal1<A>, QSignalEmitter.Signal2<A,B>, QSignalEmitter.Signal3<A,B,C>, QSignalEmitter.Signal4<A,B,C,D>, QSignalEmitter.Signal5<A,B,C,D,E>, QSignalEmitter.Signal6<A,B,C,D,E,F>, QSignalEmitter.Signal7<A,B,C,D,E,F,G>, QSignalEmitter.Signal8<A,B,C,D,E,F,G,H>, QSignalEmitter.Signal9<A,B,C,D,E,F,G,H,I>
 
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
 double det()
          Returns the matrix's determinant.
 double dx()
          Returns the horizontal translation factor.
 double dy()
          Returns the vertical translation factor.
 boolean equals(java.lang.Object other)
          
static QMatrix fromNativePointer(QNativePointer nativePointer)
          This function returns the QMatrix instance pointed to by nativePointer
 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)
          Creates and returns a QLine object that is a copy of the given l, mapped into the coordinate system defined by this matrix.
 QLineF map(QLineF l)
          Creates and returns a QLineF object that is a copy of the given l, mapped into the coordinate system defined by this matrix.
 QPainterPath map(QPainterPath p)
          Creates and returns a QPainterPath object that is a copy of the given p, mapped into the coordinate system defined by this matrix.
 QPoint map(QPoint p)
          Creates and returns a QPoint object that is a copy of the given p, mapped into the coordinate system defined by this matrix.
 QPointF map(QPointF p)
          Creates and returns a QPointF object that is a copy of the given p, mapped into the coordinate system defined by this matrix.
 QPolygon map(QPolygon a)
          Creates and returns a QPolygon object that is a copy of the given a, mapped into the coordinate system defined by this matrix.
 QPolygonF map(QPolygonF a)
          Creates and returns a QPolygonF object that is a copy of the given a, mapped into the coordinate system defined by this matrix.
 QRegion map(QRegion r)
          Creates and returns a QRegion object that is a copy of the given r, mapped into the coordinate system defined by this matrix.
 QRect mapRect(QRect arg__1)
          Creates and returns a QRect object that is a copy of the given arg__1, mapped into the coordinate system defined by this matrix.
 QRectF mapRect(QRectF arg__1)
          Creates and returns a QRectF object that is a copy of the given arg__1, mapped into the coordinate system defined by this matrix.
 QPolygon mapToPolygon(QRect r)
          Creates and returns a QPolygon representation of the given r, mapped into the coordinate system defined by this matrix.
 QMatrix multiplied(QMatrix other)
          Returns the result of multiplying this matrix by other.
 QMatrix multiply(QMatrix other)
          Returns the result of multiplying this matrix by other, and also store the result in this QMatrix.
static QNativePointer nativePointerArray(QMatrix[] array)
          This function returns a QNativePointer that is pointing to the specified QMatrix array.
 void readFrom(QDataStream arg__1)
          Reads a QMatrix from arg__1.
 void reset()
          Resets the matrix to an identity matrix, i.e. all elements are set to zero, except m11 and m22 (specifying the scale) which are set to 1.
 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.
 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 to arg__1.
 
Methods inherited from class com.trolltech.qt.QtJambiObject
dispose, disposed, finalize, reassignNativeResources, tr, tr, tr
 
Methods inherited from class com.trolltech.qt.QSignalEmitter
blockSignals, disconnect, disconnect, signalsBlocked, signalSender, thread
 
Methods inherited from class java.lang.Object
clone, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 
Methods inherited from interface com.trolltech.qt.QtJambiInterface
disableGarbageCollection, nativeId, nativePointer, reenableGarbageCollection, setJavaOwnership
 

Constructor Detail

QMatrix

public QMatrix(QMatrix matrix)

Constructs a matrix that is a copy of the given matrix.


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(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, Matrix Operations

dy

public final double dy()

Returns the vertical translation factor.

See Also:
translate, 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, Matrix Operations

m12

public final double m12()

Returns the vertical shearing factor.

See Also:
shear, Matrix Operations

m21

public final double m21()

Returns the horizontal shearing factor.

See Also:
shear, Matrix Operations

m22

public final double m22()

Returns the vertical scaling factor.

See Also:
scale, Matrix Operations

map

public final QLine map(QLine l)

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


map

public final QPolygon map(QPolygon a)

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


map

public final QRegion map(QRegion r)

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

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


map

public final QPainterPath map(QPainterPath p)

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


map

public final QPoint map(QPoint p)

Creates and returns a QPoint object that is a copy of the given p, 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)

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


map

public final QPolygonF map(QPolygonF a)

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


map

public final QPointF map(QPointF p)

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


mapRect

public final QRect mapRect(QRect arg__1)

Creates and returns a QRect object that is a copy of the given arg__1, 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 arg__1, mapped into the coordinate system defined by this matrix.

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

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

If rotation or shearing has been specified, this function returns the bounding rectangle. To retrieve the exact region the given arg__1 maps to, use the mapToPolygon function instead.

See Also:
mapToPolygon, Matrix Operations

mapToPolygon

public final QPolygon mapToPolygon(QRect r)

Creates and returns a QPolygon representation of the given r, mapped into the coordinate system defined by this matrix.

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

    x' = m11*x + m21*y + dx
    y' = m22*y + m12*x + 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, Matrix Operations

writeTo

public final void writeTo(QDataStream arg__1)
Writes thisQMatrix to arg__1.


readFrom

public final void readFrom(QDataStream arg__1)
Reads a QMatrix from arg__1.


reset

public final void reset()

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

See Also:
QMatrix, isIdentity, 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

fromNativePointer

public static QMatrix fromNativePointer(QNativePointer nativePointer)
This function returns the QMatrix instance pointed to by nativePointer

Parameters:
nativePointer - the QNativePointer of which object should be returned.

nativePointerArray

public static QNativePointer nativePointerArray(QMatrix[] array)
This function returns a QNativePointer that is pointing to the specified QMatrix array.

Parameters:
array - the array that the returned pointer will point to.
Returns:
a QNativePointer that is pointing to the specified array.

equals

public boolean equals(java.lang.Object other)

Overrides:
equals in class java.lang.Object

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.

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.


multiply

public final QMatrix multiply(QMatrix other)
Returns the result of multiplying this matrix by other, and also store the result in this QMatrix.


multiplied

public final QMatrix multiplied(QMatrix other)
Returns the result of multiplying this matrix by other.


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