QTransform

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

Inheritance diagram of PySide2.QtGui.QTransform

Synopsis

Functions

Static functions

Detailed Description

A transformation specifies how to translate, scale, shear, rotate or project the coordinate system, and is typically used when rendering graphics.

QTransform differs from QMatrix in that it is a true 3x3 matrix, allowing perspective transformations. QTransform ‘s toAffine() method allows casting QTransform to QMatrix . If a perspective transformation has been specified on the matrix, then the conversion will cause loss of data.

QTransform is the recommended transformation class in Qt.

A QTransform 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 QTransform 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.

QTransform 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), and adjoint() returns the matrix’s classical adjoint. In addition, QTransform provides the determinant() function which returns the matrix’s determinant.

Finally, the QTransform class supports matrix multiplication, addition and subtraction, 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 QTransform . For example:

qtransform-simpletransformation1

def paintEvent(self, event)
    painter = QPainter(self)
    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, "QTransform")

Although these functions are very convenient, it can be more efficient to build a QTransform and call setTransform() if you want to perform more than a single transform operation. For example:

qtransform-combinedtransformation2

def paintEvent(self, event)
    painter = QPainter(self)
    painter.setPen(QPen(Qt.blue, 1, Qt.DashLine))
    painter.drawRect(0, 0, 100, 100)

    transform = QTransform()
    transform.translate(50, 50)
    transform.rotate(45)
    transform.scale(0.5, 1.0)
    painter.setTransform(transform)

    painter.setFont(QFont("Helvetica", 24))
    painter.setPen(QPen(Qt.black, 1))
    painter.drawText(20, 10, "QTransform")

Basic Matrix Operations

../../_images/qtransform-representation.png

A QTransform object contains a 3 x 3 matrix. The m31 (dx ) and m32 (dy ) elements specify horizontal and vertical translation. The m11 and m22 elements specify horizontal and vertical scaling. The m21 and m12 elements specify horizontal and vertical shearing . And finally, the m13 and m23 elements specify horizontal and vertical projection, with m33 as an additional projection factor.

QTransform 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
if is not affine:
    w' = m13*x + m23*y + m33
    x' /= w'
    y' /= w'

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() , m13() , m21() , m22() , m23() , m31() , m32() , m33() , 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 , m22 , and m33 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 setting both the shearing factors and the scaling factors. Perspective transformation is achieved by setting both the projection factors and the scaling factors.

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

qtransform-combinedtransformation23

def paintEvent(self, event)
    pi = 3.14

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

    translationTransform = QTransform(1, 0, 0, 1, 50.0, 50.0)
    rotationTransform = QTransform(cosa, sina, -sina, cosa, 0, 0)
    scalingTransform = QTransform(0.5, 0, 0, 1.0, 0, 0)

    transform = QTransform()
    transform = scalingTransform * rotationTransform * translationTransform

    painter = QPainter(self)
    painter.setPen(QPen(Qt.blue, 1, Qt.DashLine))
    painter.drawRect(0, 0, 100, 100)

    painter.setTransform(transform)

    painter.setFont(QFont("Helvetica", 24))
    painter.setPen(QPen(Qt.black, 1))
    painter.drawText(20, 10, "QTransform")
class QTransform

QTransform(mtx)

QTransform(other)

QTransform(h11, h12, h13, h21, h22, h23, h31, h32[, h33=1.0])

QTransform(h11, h12, h21, h22, dx, dy)

param h32

qreal

param h33

qreal

param h21

qreal

param h22

qreal

param h23

qreal

param mtx

QMatrix

param h11

qreal

param h12

qreal

param h13

qreal

param dx

qreal

param dy

qreal

param other

QTransform

param h31

qreal

Constructs an identity matrix.

All elements are set to zero except m11 and m22 (specifying the scale) and m33 which are set to 1.

See also

reset()

Constructs a matrix with the elements, m11 , m12 , m13 , m21 , m22 , m23 , m31 , m32 , m33 .

See also

setMatrix()

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

See also

setMatrix()

PySide2.QtGui.QTransform.TransformationType

Constant

Description

QTransform.TxNone

QTransform.TxTranslate

QTransform.TxScale

QTransform.TxRotate

QTransform.TxShear

QTransform.TxProject

PySide2.QtGui.QTransform.__reduce__()
Return type

PyObject

PySide2.QtGui.QTransform.__repr__()
Return type

PyObject

PySide2.QtGui.QTransform.adjoint()
Return type

QTransform

Returns the adjoint of this matrix.

PySide2.QtGui.QTransform.det()
Return type

qreal

Note

This function is deprecated.

Returns the matrix’s determinant. Use determinant() instead.

PySide2.QtGui.QTransform.determinant()
Return type

qreal

Returns the matrix’s determinant.

PySide2.QtGui.QTransform.dx()
Return type

qreal

Returns the horizontal translation factor.

See also

m31() translate() Basic Matrix Operations

PySide2.QtGui.QTransform.dy()
Return type

qreal

Returns the vertical translation factor.

See also

translate() Basic Matrix Operations

static PySide2.QtGui.QTransform.fromScale(dx, dy)
Parameters
  • dxqreal

  • dyqreal

Return type

QTransform

Creates a matrix which corresponds to a scaling of sx horizontally and sy vertically. This is the same as QTransform() .scale(sx, sy) but slightly faster.

static PySide2.QtGui.QTransform.fromTranslate(dx, dy)
Parameters
  • dxqreal

  • dyqreal

Return type

QTransform

Creates a matrix which corresponds to a translation of dx along the x axis and dy along the y axis. This is the same as QTransform() .translate(dx, dy) but slightly faster.

PySide2.QtGui.QTransform.inverted()
Return type

PyTuple

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()

PySide2.QtGui.QTransform.isAffine()
Return type

bool

Returns true if the matrix represent an affine transformation, otherwise returns false .

PySide2.QtGui.QTransform.isIdentity()
Return type

bool

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

See also

reset()

PySide2.QtGui.QTransform.isInvertible()
Return type

bool

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

See also

inverted()

PySide2.QtGui.QTransform.isRotating()
Return type

bool

Returns true if the matrix represents some kind of a rotating transformation, otherwise returns false .

Note

A rotation transformation of 180 degrees and/or 360 degrees is treated as a scaling transformation.

See also

reset()

PySide2.QtGui.QTransform.isScaling()
Return type

bool

Returns true if the matrix represents a scaling transformation, otherwise returns false .

See also

reset()

PySide2.QtGui.QTransform.isTranslating()
Return type

bool

Returns true if the matrix represents a translating transformation, otherwise returns false .

See also

reset()

PySide2.QtGui.QTransform.m11()
Return type

qreal

Returns the horizontal scaling factor.

See also

scale() Basic Matrix Operations

PySide2.QtGui.QTransform.m12()
Return type

qreal

Returns the vertical shearing factor.

See also

shear() Basic Matrix Operations

PySide2.QtGui.QTransform.m13()
Return type

qreal

Returns the horizontal projection factor.

See also

translate() Basic Matrix Operations

PySide2.QtGui.QTransform.m21()
Return type

qreal

Returns the horizontal shearing factor.

See also

shear() Basic Matrix Operations

PySide2.QtGui.QTransform.m22()
Return type

qreal

Returns the vertical scaling factor.

See also

scale() Basic Matrix Operations

PySide2.QtGui.QTransform.m23()
Return type

qreal

Returns the vertical projection factor.

See also

translate() Basic Matrix Operations

PySide2.QtGui.QTransform.m31()
Return type

qreal

Returns the horizontal translation factor.

See also

dx() translate() Basic Matrix Operations

PySide2.QtGui.QTransform.m32()
Return type

qreal

Returns the vertical translation factor.

See also

dy() translate() Basic Matrix Operations

PySide2.QtGui.QTransform.m33()
Return type

qreal

Returns the division factor.

See also

translate() Basic Matrix Operations

PySide2.QtGui.QTransform.map(x, y)
Parameters
  • xqreal

  • yqreal

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
if is not affine:
    w' = m13*x + m23*y + m33
    x' /= w'
    y' /= w'

The point (x, y) is the original point, and (x’, y’) is the transformed point.

See also

Basic Matrix Operations

PySide2.QtGui.QTransform.map(r)
Parameters

rQRegion

Return type

QRegion

PySide2.QtGui.QTransform.map(a)
Parameters

aQPolygonF

Return type

QPolygonF

PySide2.QtGui.QTransform.map(a)
Parameters

aQPolygon

Return type

QPolygon

PySide2.QtGui.QTransform.map(p)
Parameters

pQPoint

Return type

QPoint

PySide2.QtGui.QTransform.map(p)
Parameters

pQPointF

Return type

QPointF

PySide2.QtGui.QTransform.map(l)
Parameters

lQLine

Return type

QLine

PySide2.QtGui.QTransform.map(p)
Parameters

pQPainterPath

Return type

QPainterPath

PySide2.QtGui.QTransform.map(l)
Parameters

lQLineF

Return type

QLineF

PySide2.QtGui.QTransform.mapRect(arg__1)
Parameters

arg__1QRect

Return type

QRect

PySide2.QtGui.QTransform.mapRect(arg__1)
Parameters

arg__1QRectF

Return type

QRectF

PySide2.QtGui.QTransform.mapToPolygon(r)
Parameters

rQRect

Return type

QPolygon

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
if is not affine:
    w' = m13*x + m23*y + m33
    x' /= w'
    y' /= w'

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() Basic Matrix Operations

PySide2.QtGui.QTransform.__ne__(arg__1)
Parameters

arg__1QTransform

Return type

bool

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

PySide2.QtGui.QTransform.__mul__(n)
Parameters

nqreal

Return type

QTransform

PySide2.QtGui.QTransform.__mul__(o)
Parameters

oQTransform

Return type

QTransform

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

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

PySide2.QtGui.QTransform.__imul__(arg__1)
Parameters

arg__1QTransform

Return type

QTransform

PySide2.QtGui.QTransform.__imul__(div)
Parameters

divqreal

Return type

QTransform

This is an overloaded function.

Returns the result of performing an element-wise multiplication of this matrix with the given scalar .

PySide2.QtGui.QTransform.__add__(n)
Parameters

nqreal

Return type

QTransform

PySide2.QtGui.QTransform.__iadd__(div)
Parameters

divqreal

Return type

QTransform

This is an overloaded function.

Returns the matrix obtained by adding the given scalar to each element of this matrix.

PySide2.QtGui.QTransform.__sub__(n)
Parameters

nqreal

Return type

QTransform

PySide2.QtGui.QTransform.__isub__(div)
Parameters

divqreal

Return type

QTransform

This is an overloaded function.

Returns the matrix obtained by subtracting the given scalar from each element of this matrix.

PySide2.QtGui.QTransform.__div__(n)
Parameters

nqreal

Return type

QTransform

PySide2.QtGui.QTransform.__idiv__(div)
Parameters

divqreal

Return type

QTransform

This is an overloaded function.

Returns the result of performing an element-wise division of this matrix by the given scalar .

PySide2.QtGui.QTransform.__eq__(arg__1)
Parameters

arg__1QTransform

Return type

bool

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

static PySide2.QtGui.QTransform.quadToQuad(arg__1, arg__2)
Parameters
Return type

PyObject

static PySide2.QtGui.QTransform.quadToQuad(one, two, result)
Parameters
Return type

bool

Creates a transformation matrix, trans , that maps a four-sided polygon, one , to another four-sided polygon, two . Returns true if the transformation is possible; otherwise returns false.

This is a convenience method combining quadToSquare() and squareToQuad() methods. It allows the input quad to be transformed into any other quad.

See also

squareToQuad() quadToSquare()

static PySide2.QtGui.QTransform.quadToSquare(arg__1)
Parameters

arg__1QPolygonF

Return type

PyObject

static PySide2.QtGui.QTransform.quadToSquare(quad, result)
Parameters
Return type

bool

Creates a transformation matrix, trans , that maps a four-sided polygon, quad , to a unit square. Returns true if the transformation is constructed or false if such a transformation does not exist.

See also

squareToQuad() quadToQuad()

PySide2.QtGui.QTransform.reset()

Resets the matrix to an identity matrix, i.e. all elements are set to zero, except m11 and m22 (specifying the scale) and m33 which are set to 1.

See also

QTransform() isIdentity() Basic Matrix Operations

PySide2.QtGui.QTransform.rotate(a[, axis=Qt.ZAxis])
Parameters
  • aqreal

  • axisAxis

Return type

QTransform

Rotates the coordinate system counterclockwise by the given angle about the specified axis and returns a reference to the matrix.

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

The angle is specified in degrees.

See also

setMatrix()

PySide2.QtGui.QTransform.rotateRadians(a[, axis=Qt.ZAxis])
Parameters
  • aqreal

  • axisAxis

Return type

QTransform

Rotates the coordinate system counterclockwise by the given angle about the specified axis and returns a reference to the matrix.

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

The angle is specified in radians.

See also

setMatrix()

PySide2.QtGui.QTransform.scale(sx, sy)
Parameters
  • sxqreal

  • syqreal

Return type

QTransform

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

See also

setMatrix()

PySide2.QtGui.QTransform.setMatrix(m11, m12, m13, m21, m22, m23, m31, m32, m33)
Parameters
  • m11qreal

  • m12qreal

  • m13qreal

  • m21qreal

  • m22qreal

  • m23qreal

  • m31qreal

  • m32qreal

  • m33qreal

Sets the matrix elements to the specified values, m11 , m12 , m13 m21 , m22 , m23 m31 , m32 and m33 . Note that this function replaces the previous values. QTransform provides the translate() , rotate() , scale() and shear() convenience functions to manipulate the various matrix elements based on the currently defined coordinate system.

See also

QTransform()

PySide2.QtGui.QTransform.shear(sh, sv)
Parameters
  • shqreal

  • svqreal

Return type

QTransform

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

See also

setMatrix()

static PySide2.QtGui.QTransform.squareToQuad(arg__1)
Parameters

arg__1QPolygonF

Return type

PyObject

static PySide2.QtGui.QTransform.squareToQuad(square, result)
Parameters
Return type

bool

Creates a transformation matrix, trans , that maps a unit square to a four-sided polygon, quad . Returns true if the transformation is constructed or false if such a transformation does not exist.

See also

quadToSquare() quadToQuad()

PySide2.QtGui.QTransform.toAffine()
Return type

QMatrix

Returns the QTransform as an affine matrix.

Warning

If a perspective transformation has been specified, then the conversion will cause loss of data.

PySide2.QtGui.QTransform.translate(dx, dy)
Parameters
  • dxqreal

  • dyqreal

Return type

QTransform

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()

PySide2.QtGui.QTransform.transposed()
Return type

QTransform

Returns the transpose of this matrix.

PySide2.QtGui.QTransform.type()
Return type

TransformationType

Returns the transformation type of this matrix.

The transformation type is the highest enumeration value capturing all of the matrix’s transformations. For example, if the matrix both scales and shears, the type would be TxShear , because TxShear has a higher enumeration value than TxScale .

Knowing the transformation type of a matrix is useful for optimization: you can often handle specific types more optimally than handling the generic case.