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# QMatrix Class Reference
[QtGui module]

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

### Methods

- __init__ (self)
- __init__ (self, float m11, float m12, float m21, float m22, float dx, float dy)
- __init__ (self, QMatrix matrix)
- float det (self)
- float dx (self)
- float dy (self)
- (QMatrix, bool invertible) inverted (self)
- bool isIdentity (self)
- bool isInvertible (self)
- float m11 (self)
- float m12 (self)
- float m21 (self)
- float m22 (self)
- (int tx, int ty) map (self, int x, int y)
- (float tx, float ty) map (self, float x, float y)
- QPoint map (self, QPoint p)
- QPointF map (self, QPointF p)
- QLine map (self, QLine l)
- QLineF map (self, QLineF l)
- QPolygonF map (self, QPolygonF a)
- QPolygon map (self, QPolygon a)
- QRegion map (self, QRegion r)
- QPainterPath map (self, QPainterPath p)
- QRect mapRect (self, QRect)
- QRectF mapRect (self, QRectF)
- QPolygon mapToPolygon (self, QRect r)
- reset (self)
- QMatrix rotate (self, float a)
- QMatrix scale (self, float sx, float sy)
- setMatrix (self, float m11, float m12, float m21, float m22, float dx, float dy)
- QMatrix shear (self, float sh, float sv)
- QMatrix translate (self, float dx, float dy)

### Special Methods

- bool __eq__ (self, QMatrix)
- QMatrix __imul__ (self, QMatrix)
- QMatrix __mul__ (self, QMatrix o)
- bool __ne__ (self, QMatrix)

## 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.

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
- Basic Matrix Operations

### 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, Affine Transformations Demo, and Transformations Example.

## Method Documentation

### QMatrix.__init__ (self)

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.__init__ (self, float m11, float m12, float m21, float m22, float dx, float dy)

Constructs a matrix with the elements, m11, m12, m21, m22, dx and dy.

See also setMatrix().

### QMatrix.__init__ (self, QMatrix matrix)

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

### float QMatrix.det (self)

Returns the matrix's determinant.

### float QMatrix.dx (self)

Returns the horizontal translation factor.

See also translate() and Basic Matrix Operations.

### float QMatrix.dy (self)

Returns the vertical translation factor.

See also translate() and Basic Matrix Operations.

### (QMatrix, bool invertible) QMatrix.inverted (self)

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().

### bool QMatrix.isIdentity (self)

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

See also reset().

### bool QMatrix.isInvertible (self)

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

See also inverted().

### float QMatrix.m11 (self)

Returns the horizontal scaling factor.

See also scale() and Basic Matrix Operations.

### float QMatrix.m12 (self)

Returns the vertical shearing factor.

See also shear() and Basic Matrix Operations.

### float QMatrix.m21 (self)

Returns the horizontal shearing factor.

See also shear() and Basic Matrix Operations.

### float QMatrix.m22 (self)

Returns the vertical scaling factor.

See also scale() and Basic Matrix Operations.

### (int tx, int ty) QMatrix.map (self, int x, int y)

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.

### (float tx, float ty) QMatrix.map (self, float x, float y)

### QPoint QMatrix.map (self, QPoint p)

This is an overloaded member function, provided for convenience.

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.

### QPointF QMatrix.map (self, 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.

### QLine QMatrix.map (self, QLine l)

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.

### QLineF QMatrix.map (self, 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.

### QPolygonF QMatrix.map (self, QPolygonF a)

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.

### QPolygon QMatrix.map (self, QPolygon 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.

### QRegion QMatrix.map (self, QRegion r)

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.

### QPainterPath QMatrix.map (self, QPainterPath p)

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.

### QRect QMatrix.mapRect (self, QRect)

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.

### QRectF QMatrix.mapRect (self, QRectF)

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.

### QPolygon QMatrix.mapToPolygon (self, 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.

### QMatrix.reset (self)

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.

### QMatrix QMatrix.rotate (self, float 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().

### QMatrix QMatrix.scale (self, float sx, float sy)

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

See also setMatrix().

### QMatrix.setMatrix (self, float m11, float m12, float m21, float m22, float dx, float 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().

### QMatrix QMatrix.shear (self, float sh, float sv)

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

See also setMatrix().

### QMatrix QMatrix.translate (self, float dx, float 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().

### bool QMatrix.__eq__ (self, QMatrix)

### QMatrix QMatrix.__imul__ (self, QMatrix)

### QMatrix QMatrix.__mul__ (self, QMatrix o)

### bool QMatrix.__ne__ (self, QMatrix)