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# QTransform Class Reference
[QtGui module]

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

### Types

- enum TransformationType { TxNone, TxTranslate, TxScale, TxRotate, TxShear, TxProject }

### Methods

- __init__ (self)
- __init__ (self, float, float, float, float, float, float, float, float, float m33 = 1)
- __init__ (self, float, float, float, float, float, float)
- __init__ (self, QMatrix)
- __init__ (self, QTransform)
- QTransform adjoint (self)
- float det (self)
- float determinant (self)
- float dx (self)
- float dy (self)
- (QTransform, bool invertible) inverted (self)
- bool isAffine (self)
- bool isIdentity (self)
- bool isInvertible (self)
- bool isRotating (self)
- bool isScaling (self)
- bool isTranslating (self)
- float m11 (self)
- float m12 (self)
- float m13 (self)
- float m21 (self)
- float m22 (self)
- float m23 (self)
- float m31 (self)
- float m32 (self)
- float m33 (self)
- (int, int) map (self, int, int)
- (float, float) map (self, float, float)
- QPoint map (self, QPoint)
- QPointF map (self, QPointF)
- QLine map (self, QLine)
- QLineF map (self, QLineF)
- QPolygonF map (self, QPolygonF)
- QPolygon map (self, QPolygon)
- QRegion map (self, QRegion)
- QPainterPath map (self, QPainterPath)
- QRect mapRect (self, QRect)
- QRectF mapRect (self, QRectF)
- QPolygon mapToPolygon (self, QRect)
- reset (self)
- QTransform rotate (self, float, Qt.Axis axis = Qt.ZAxis)
- QTransform rotateRadians (self, float, Qt.Axis axis = Qt.ZAxis)
- QTransform scale (self, float, float)
- setMatrix (self, float, float, float, float, float, float, float, float, float)
- QTransform shear (self, float, float)
- QMatrix toAffine (self)
- QTransform translate (self, float, float)
- QTransform transposed (self)
- TransformationType type (self)

### Static Methods

- QTransform fromScale (float, float)
- QTransform fromTranslate (float, float)
- bool quadToQuad (QPolygonF, QPolygonF, QTransform)
- bool quadToSquare (QPolygonF, QTransform)
- bool squareToQuad (QPolygonF, QTransform)

### Special Methods

- QTransform __add__ (self, float)
- QTransform __div__ (self, float)
- bool __eq__ (self, QTransform)
- QTransform __iadd__ (self, float)
- QTransform __idiv__ (self, float)
- QTransform __imul__ (self, QTransform)
- QTransform __imul__ (self, float)
- QTransform __isub__ (self, float)
- QTransform __mul__ (self, float)
- QTransform __mul__ (self, QTransform)
- bool __ne__ (self, QTransform)
- QTransform __sub__ (self, float)

## Detailed Description

This class can be pickled.

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

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(obsolete) in that it is a true 3x3 matrix, allowing perspective transformations. QTransform's toAffine() method allows casting QTransform to QMatrix(obsolete). 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
- 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 QTransform. 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, "QTransform");
     }

Although these functions are very convenient, it can be more efficient to build a QTransform and call QPainter.setTransform() 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);

         QTransform transform;
         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

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:

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

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

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

         QTransform transform;
         transform = scalingTransform * rotationTransform * translationTransform;

         QPainter painter(this);
         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");
     }

See also QPainter, The Coordinate System, Affine Transformations Demo, and Transformations Example.

## Type Documentation

### QTransform.TransformationType

Constant | Value
--- | ---
`QTransform.TxNone` | `0x00`
`QTransform.TxTranslate` | `0x01`
`QTransform.TxScale` | `0x02`
`QTransform.TxRotate` | `0x04`
`QTransform.TxShear` | `0x08`
`QTransform.TxProject` | `0x10`

## Method Documentation

### QTransform.__init__ (self)

Constructs an identity matrix.

All elements are set to zero except `m11` and `m22` (specifying the scale) and `m13` which are set to 1.

See also reset().

### QTransform.__init__ (self, float, float, float, float, float, float, float, float, float m33 = 1)

### QTransform.__init__ (self, float, float, float, float, float, float)

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

See also setMatrix().

### QTransform.__init__ (self, QMatrix)

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

See also setMatrix().

### QTransform.__init__ (self, QTransform)

Constructs a matrix that is a copy of the given matrix. Note that the `m13`, `m23`, and `m33` elements are set to 0, 0, and 1 respectively.

### QTransform QTransform.adjoint (self)

Returns the adjoint of this matrix.

### float QTransform.det (self)

### float QTransform.determinant (self)

Returns the matrix's determinant.

### float QTransform.dx (self)

Returns the horizontal translation factor.

See also m31(), translate(), and Basic Matrix Operations.

### float QTransform.dy (self)

Returns the vertical translation factor.

See also translate() and Basic Matrix Operations.

### QTransform QTransform.fromScale (float, float)

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.

This function was introduced in Qt 4.5.

### QTransform QTransform.fromTranslate (float, float)

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.

This function was introduced in Qt 4.5.

### (QTransform, bool invertible) QTransform.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 QTransform.isAffine (self)

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

### bool QTransform.isIdentity (self)

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

See also reset().

### bool QTransform.isInvertible (self)

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

See also inverted().

### bool QTransform.isRotating (self)

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

See also reset().

### bool QTransform.isScaling (self)

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

See also reset().

### bool QTransform.isTranslating (self)

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

See also reset().

### float QTransform.m11 (self)

Returns the horizontal scaling factor.

See also scale() and Basic Matrix Operations.

### float QTransform.m12 (self)

Returns the vertical shearing factor.

See also shear() and Basic Matrix Operations.

### float QTransform.m13 (self)

Returns the horizontal projection factor.

See also translate() and Basic Matrix Operations.

### float QTransform.m21 (self)

Returns the horizontal shearing factor.

See also shear() and Basic Matrix Operations.

### float QTransform.m22 (self)

Returns the vertical scaling factor.

See also scale() and Basic Matrix Operations.

### float QTransform.m23 (self)

Returns the vertical projection factor.

See also translate() and Basic Matrix Operations.

### float QTransform.m31 (self)

Returns the horizontal translation factor.

See also dx(), translate(), and Basic Matrix Operations.

### float QTransform.m32 (self)

Returns the vertical translation factor.

See also dy(), translate(), and Basic Matrix Operations.

### float QTransform.m33 (self)

Returns the division factor.

See also translate() and Basic Matrix Operations.

### (int, int) QTransform.map (self, int, int)

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.

### (float, float) QTransform.map (self, float, float)

This is an overloaded function.

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

### QPoint QTransform.map (self, QPoint)

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.

### QPointF QTransform.map (self, QPointF)

This is an overloaded function.

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

### QLine QTransform.map (self, QLine)

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.

### QLineF QTransform.map (self, QLineF)

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.

### QPolygonF QTransform.map (self, QPolygonF)

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.

### QPolygon QTransform.map (self, QPolygon)

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.

### QRegion QTransform.map (self, QRegion)

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.

### QPainterPath QTransform.map (self, QPainterPath)

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.

### QRect QTransform.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 (is not affine) {
         w' = m13*x + m23*y + m33
         x' /= w'
         y' /= w'
     }

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 QTransform.mapRect (self, QRectF)

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.

### QPolygon QTransform.mapToPolygon (self, QRect)

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() and Basic Matrix Operations.

### bool QTransform.quadToQuad (QPolygonF, QPolygonF, QTransform)

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() and quadToSquare().

### bool QTransform.quadToSquare (QPolygonF, QTransform)

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() and quadToQuad().

### QTransform.reset (self)

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(), and Basic Matrix Operations.

### QTransform QTransform.rotate (self, float, Qt.Axis axis = Qt.ZAxis)

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().

### QTransform QTransform.rotateRadians (self, float, Qt.Axis axis = Qt.ZAxis)

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().

### QTransform QTransform.scale (self, float, float)

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

See also setMatrix().

### QTransform.setMatrix (self, float, float, float, float, float, float, float, float, float)

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().

### QTransform QTransform.shear (self, float, float)

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

See also setMatrix().

### bool QTransform.squareToQuad (QPolygonF, QTransform)

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() and quadToQuad().

### QMatrix QTransform.toAffine (self)

Returns the QTransform as an affine matrix.

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

### QTransform QTransform.translate (self, float, float)

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().

### QTransform QTransform.transposed (self)

Returns the transpose of this matrix.

### TransformationType QTransform.type (self)

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.

### QTransform QTransform.__add__ (self, float)

### QTransform QTransform.__div__ (self, float)

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

### QTransform QTransform.__iadd__ (self, float)

### QTransform QTransform.__idiv__ (self, float)

### QTransform QTransform.__imul__ (self, QTransform)

### QTransform QTransform.__imul__ (self, float)

### QTransform QTransform.__isub__ (self, float)

### QTransform QTransform.__mul__ (self, float)

### QTransform QTransform.__mul__ (self, QTransform)

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

### QTransform QTransform.__sub__ (self, float)