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

**__init__**(*self*)- float
**det**(*self*) - float
**determinant**(*self*) - float
**dx**(*self*) - float
**dy**(*self*) - bool
**isIdentity**(*self*) - bool
**isInvertible**(*self*) - float
**m11**(*self*) - float
**m12**(*self*) - float
**m21**(*self*) - float
**m22**(*self*) - QRect
**mapRect**(*self*, QRect) - QRectF
**mapRect**(*self*, QRectF) **reset**(*self*)

This class can be pickled.

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.

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"); } |

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"); } |

Constructs an identity matrix.

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

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

**See also** setMatrix().

Returns the matrix's determinant.

This function was introduced in Qt 4.6.

Returns the horizontal translation factor.

**See also** translate()
and Basic Matrix Operations.

Returns the vertical translation factor.

**See also** translate()
and Basic Matrix Operations.

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().

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

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

Returns the horizontal scaling factor.

**See also** scale() and
Basic Matrix Operations.

Returns the vertical shearing factor.

**See also** shear() and
Basic Matrix Operations.

Returns the horizontal shearing factor.

**See also** shear() and
Basic Matrix Operations.

Returns the vertical scaling factor.

**See also** scale() and
Basic Matrix Operations.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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().

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

**See also** setMatrix().

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().

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

**See also** setMatrix().

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().

PyQt 4.12.1 for X11 | Copyright © Riverbank Computing Ltd and The Qt Company 2015 | Qt 4.8.7 |