QtGui.QMatrix Class Reference

The QMatrix class specifies 2D transformations of a coordinate system. More...

Inheritance diagram for QtGui.QMatrix:

Collaboration diagram for QtGui.QMatrix:

Public Member Functions
override bool	Equals (object o)
override int	GetHashCode ()
	QMatrix ()
	QMatrix (QMatrix matrix)
	QMatrix (Qt.Initialization arg1)
	QMatrix (double m11, double m12, double m21, double m22, double dx, double dy)
virtual void	CreateProxy ()
new double	Det ()
new double	Determinant ()
new double	Dx ()
new double	Dy ()
new QMatrix	Inverted ()
new QMatrix	Inverted (ref bool invertible)
new bool	IsIdentity ()
new bool	IsInvertible ()
new double	M11 ()
new double	M12 ()
new double	M21 ()
new double	M22 ()
new QPoint	Map (QPoint p)
new QPointF	Map (QPointF p)
new QLine	Map (QLine l)
new QLineF	Map (QLineF l)
new QPolygonF	Map (QPolygonF a)
new QPolygon	Map (QPolygon a)
new QRegion	Map (QRegion r)
new QPainterPath	Map (QPainterPath p)
new void	Map (int x, int y, ref int tx, ref int ty)
new void	Map (double x, double y, ref double tx, ref double ty)
new QRect	MapRect (QRect arg1)
new QRectF	MapRect (QRectF arg1)
new QPolygon	MapToPolygon (QRect r)
new void	Reset ()
new QMatrix	Rotate (double a)
new QMatrix	Scale (double sx, double sy)
new void	SetMatrix (double m11, double m12, double m21, double m22, double dx, double dy)
new QMatrix	Shear (double sh, double sv)
new QMatrix	Translate (double dx, double dy)
new void	Dispose ()

Static Public Member Functions
static bool	operator!= (QMatrix arg1, QMatrix arg2)
static QMatrix	operator* (QMatrix arg1, QMatrix arg2)
static bool	operator== (QMatrix arg1, QMatrix arg2)

Protected Member Functions
	QMatrix (System.Type dummy)

Protected Attributes
SmokeInvocation	interceptor

Properties
virtual System.IntPtr	SmokeObject [get, set]

Detailed Description

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. QMatrix, in contrast to QTransform, does not allow perspective transformations. QTransform is the recommended transformation class in Qt.

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 determinant() 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 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:

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, QTransform, Coordinate System, Affine Transformations Demo, and Transformations Example.

Constructor & Destructor Documentation

QtGui.QMatrix.QMatrix ( System.Type  dummy )

protected

QtGui.QMatrix.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().

QtGui.QMatrix.QMatrix

(

QMatrix

matrix

)

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

QtGui.QMatrix.QMatrix

(

Qt.Initialization

arg1

)

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().

QtGui.QMatrix.QMatrix	(	double	m11,
		double	m12,
		double	m21,
		double	m22,
		double	dx,
		double	dy
	)

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().

Member Function Documentation

virtual void QtGui.QMatrix.CreateProxy ( )

virtual

new double QtGui.QMatrix.Det

(

)

new double QtGui.QMatrix.Determinant

(

)

Returns the matrix's determinant.

This function was introduced in Qt 4.6.

new void QtGui.QMatrix.Dispose

(

)

new double QtGui.QMatrix.Dx

(

)

Returns the horizontal translation factor.

See also translate() and Basic Matrix Operations.

new double QtGui.QMatrix.Dy

(

)

Returns the vertical translation factor.

See also translate() and Basic Matrix Operations.

override bool QtGui.QMatrix.Equals

(

object

o

)

override int QtGui.QMatrix.GetHashCode

(

)

new QMatrix QtGui.QMatrix.Inverted

(

)

Returns an inverted copy of this matrix.

If the matrix is singular (not invertible), the returned matrix is the identity matrix. If invertible is valid (i.e. not 0), its value is set to true if the matrix is invertible, otherwise it is set to false.

See also isInvertible().

new QMatrix QtGui.QMatrix.Inverted

(

ref bool

invertible

)

Returns an inverted copy of this matrix.

If the matrix is singular (not invertible), the returned matrix is the identity matrix. If invertible is valid (i.e. not 0), its value is set to true if the matrix is invertible, otherwise it is set to false.

See also isInvertible().

new bool QtGui.QMatrix.IsIdentity

(

)

Returns true if the matrix is the identity matrix, otherwise returns false.

See also reset().

new bool QtGui.QMatrix.IsInvertible

(

)

Returns true if the matrix is invertible, otherwise returns false.

See also inverted().

new double QtGui.QMatrix.M11

(

)

Returns the horizontal scaling factor.

See also scale() and Basic Matrix Operations.

new double QtGui.QMatrix.M12

(

)

Returns the vertical shearing factor.

See also shear() and Basic Matrix Operations.

new double QtGui.QMatrix.M21

(

)

Returns the horizontal shearing factor.

See also shear() and Basic Matrix Operations.

new double QtGui.QMatrix.M22

(

)

Returns the vertical scaling factor.

See also scale() and Basic Matrix Operations.

new QPoint QtGui.QMatrix.Map

(

QPoint

p

)

This is an overloaded function.

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.

new QPointF QtGui.QMatrix.Map

(

QPointF

p

)

This is an overloaded function.

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

new QLine QtGui.QMatrix.Map

(

QLine

l

)

This is an overloaded function.

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.

new QLineF QtGui.QMatrix.Map

(

QLineF

l

)

This is an overloaded function.

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

new QPolygonF QtGui.QMatrix.Map

(

QPolygonF

a

)

This is an overloaded function.

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

new QPolygon QtGui.QMatrix.Map

(

QPolygon

a

)

This is an overloaded function.

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.

new QRegion QtGui.QMatrix.Map

(

QRegion

r

)

This is an overloaded function.

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.

new QPainterPath QtGui.QMatrix.Map

(

QPainterPath

p

)

This is an overloaded function.

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

new void QtGui.QMatrix.Map	(	int	x,
		int	y,
		ref int	tx,
		ref int	ty
	)

This is an overloaded function.

Maps the given coordinates x and y into the coordinate system defined by this matrix. The resulting values are put in *tx and *ty, respectively. Note that the transformed coordinates are rounded to the nearest integer.

new void QtGui.QMatrix.Map	(	double	x,
		double	y,
		ref double	tx,
		ref double	ty
	)

Maps the given coordinates x and y into the coordinate system defined by this matrix. The resulting values are put in *tx and *ty, respectively.

The coordinates are transformed 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.

See also Basic Matrix Operations.

new QRect QtGui.QMatrix.MapRect

(

QRect

arg1

)

This is an overloaded function.

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.

new QRectF QtGui.QMatrix.MapRect

(

QRectF

arg1

)

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*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 rectangle maps to, use the mapToPolygon() function instead.

See also mapToPolygon() and Basic Matrix Operations.

new QPolygon QtGui.QMatrix.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*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() and Basic Matrix Operations.

static bool QtGui.QMatrix.operator!= ( QMatrix  arg1, QMatrix  arg2  )

static

Returns true if this matrix is not equal to the given matrix, otherwise returns false.

static QMatrix QtGui.QMatrix.operator* ( QMatrix  arg1, QMatrix  arg2  )

static

Returns the result of multiplying this matrix by the given matrix.

Note that matrix multiplication is not commutative, i.e. a*b != b*a.

static bool QtGui.QMatrix.operator== ( QMatrix  arg1, QMatrix  arg2  )

static

Returns true if this matrix is equal to the given matrix, otherwise returns false.

new void QtGui.QMatrix.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(), and Basic Matrix Operations.

new QMatrix QtGui.QMatrix.Rotate

(

double

a

)

Rotates the coordinate system the given 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.

See also setMatrix().

new QMatrix QtGui.QMatrix.Scale	(	double	sx,
		double	sy
	)

Scales the coordinate system by sx horizontally and sy vertically, and returns a reference to the matrix.

See also setMatrix().

new void QtGui.QMatrix.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().

new QMatrix QtGui.QMatrix.Shear	(	double	sh,
		double	sv
	)

Shears the coordinate system by sh horizontally and sv vertically, and returns a reference to the matrix.

See also setMatrix().

new QMatrix QtGui.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.

See also setMatrix().

Member Data Documentation

SmokeInvocation QtGui.QMatrix.interceptor

protected

Property Documentation

virtual System.IntPtr QtGui.QMatrix.SmokeObject

getset