QTransform Class Reference
The QTransform class specifies 2D transformations of a coordinate system.
 #include <QTransform>
This class was introduced in Qt 4.3.
Detailed Description
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 nonsingular (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 topleft 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:


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:


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:


See also QPainter, Coordinate System, Affine Transformations Demo, and Transformations Example.
Public Types
Toggle details  enum QTransform::  TransformationTypeTransformationType { TxNone , TxTranslate , TxScale , TxRotate , TxShear , TxProject 0x10 ...} { TxNone , TxTranslate , TxScale , TxRotate , TxShear , TxProject 0x10 }  
 
Look up this member in the source code. 
Public Functions
Toggle details  QTransform  QTransformQTransform () () 
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().  
Look up this member in the source code.  
Toggle details  QTransform  QTransformQTransform ( qreal m11 , qreal m12 , qreal m13 , qreal m21 , qreal m22 , qreal m23 , qreal m31 , qreal m32 , qreal m33=1.0 ...) ( qreal m11 , qreal m12 , qreal m13 , qreal m21 , qreal m22 , qreal m23 , qreal m31 , qreal m32 , qreal m33=1.0 ) 
Constructs a matrix with the elements, m11, m12, m13, m21, m22, m23, m31, m32, m33. See also setMatrix().  
Look up this member in the source code.  
Toggle details  QTransform  QTransformQTransform ( qreal m11 , qreal m12 , qreal m21 , qreal m22 , qreal dx , qreal dy ...) ( qreal m11 , qreal m12 , qreal m21 , qreal m22 , qreal dx , qreal dy ) 
Constructs a matrix with the elements, m11, m12, m21, m22, dx and dy. See also setMatrix().  
Look up this member in the source code.  
Toggle details  QTransform  QTransformQTransform ( const QMatrix &matrix ) ( const QMatrix &matrix ) 
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.  
Look up this member in the source code.  
Toggle details  qreal QTransform  m11m11 () ()const 
Returns the horizontal scaling factor. See also scale() and Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  qreal QTransform  m12m12 () ()const 
Returns the vertical shearing factor. See also shear() and Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  qreal QTransform  m13m13 () ()const 
Returns the horizontal projection factor. See also translate() and Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  qreal QTransform  m21m21 () ()const 
Returns the horizontal shearing factor. See also shear() and Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  qreal QTransform  m22m22 () ()const 
Returns the vertical scaling factor. See also scale() and Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  qreal QTransform  m23m23 () ()const 
Returns the vertical projection factor. See also translate() and Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  qreal QTransform  m31m31 () ()const 
Returns the horizontal translation factor. See also dx(), translate(), and Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  qreal QTransform  m32m32 () ()const 
Returns the vertical translation factor. See also dy(), translate(), and Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  qreal QTransform  m33m33 () ()const 
Returns the division factor. See also translate() and Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  QTransform QTransform  adjointadjoint () ()const 
Returns the adjoint of this matrix.  
Look up this member in the source code.  
Toggle details  qreal QTransform  determinantdeterminant () ()const 
Returns the matrix's determinant.  
Look up this member in the source code.  
Toggle details  qreal QTransform  dxdx () ()const 
Returns the horizontal translation factor. See also m31(), translate(), and Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  qreal QTransform  dydy () ()const 
Returns the vertical translation factor. See also translate() and Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  QTransform QTransform  fromScalefromScale ( qreal sx , qreal sy ) ( qreal sx , qreal sy ) [static] 
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.  
Look up this member in the source code.  
Toggle details  QTransform QTransform  fromTranslatefromTranslate ( qreal dx , qreal dy ) ( qreal dx , qreal dy ) [static] 
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.  
Look up this member in the source code.  
Toggle details  QTransform QTransform  invertedinverted ( bool *invertible=0 ) ( bool *invertible=0 )const 
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().  
Look up this member in the source code.  
Toggle details  bool QTransform  isAffineisAffine () ()const 
Returns true if the matrix represent an affine transformation, otherwise returns false.  
Look up this member in the source code.  
Toggle details  bool QTransform  isIdentityisIdentity () ()const 
Returns true if the matrix is the identity matrix, otherwise returns false. See also reset().  
Look up this member in the source code.  
Toggle details  bool QTransform  isInvertibleisInvertible () ()const 
Returns true if the matrix is invertible, otherwise returns false. See also inverted().  
Look up this member in the source code.  
Toggle details  bool QTransform  isRotatingisRotating () ()const 
Returns true if the matrix represents some kind of a rotating transformation, otherwise returns false. See also reset().  
Look up this member in the source code.  
Toggle details  bool QTransform  isScalingisScaling () ()const 
Returns true if the matrix represents a scaling transformation, otherwise returns false. See also reset().  
Look up this member in the source code.  
Toggle details  bool QTransform  isTranslatingisTranslating () ()const 
Returns true if the matrix represents a translating transformation, otherwise returns false. See also reset().  
Look up this member in the source code.  
Toggle details  void QTransform  mapmap ( qreal x , qreal y , qreal *tx , qreal *ty ) ( qreal x , qreal y , qreal *tx , qreal *ty )const 
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:
The point (x, y) is the original point, and (x', y') is the transformed point. See also Basic Matrix Operations.  
Look up this member in the source code.  
Toggle details  QPointF QTransform  
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.  
Look up this member in the source code.  
Toggle details  QPoint QTransform  
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.  
Look up this member in the source code.  
Toggle details  QLine QTransform  
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.  
Look up this member in the source code.  
Toggle details  QLineF QTransform  
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.  
Look up this member in the source code.  
Toggle details  QPolygonF QTransform  mapmap ( const QPolygonF &polygon ) ( const QPolygonF &polygon )const 
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.  
Look up this member in the source code.  
Toggle details  QPolygon QTransform  mapmap ( const QPolygon &polygon ) ( const QPolygon &polygon )const 
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.  
Look up this member in the source code.  
Toggle details  QRegion QTransform  mapmap ( const QRegion ®ion ) ( const QRegion ®ion )const 
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.  
Look up this member in the source code.  
Toggle details  QPainterPath QTransform  mapmap ( const QPainterPath &path ) ( const QPainterPath &path )const 
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.  
Look up this member in the source code.  
Toggle details  void QTransform  mapmap ( int x , int y , int *tx , int *ty ) ( int x , int y , int *tx , int *ty )const 
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.  
Look up this member in the source code.  
Toggle details  QRectF QTransform  mapRectmapRect ( const QRectF &rectangle ) ( const QRectF &rectangle )const 
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:
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.  
Look up this member in the source code.  
Toggle details  QRect QTransform  mapRectmapRect ( const QRect &rectangle ) ( const QRect &rectangle )const 
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.  
Look up this member in the source code.  
Toggle details  QPolygon QTransform  mapToPolygonmapToPolygon ( const QRect &rectangle ) ( const QRect &rectangle )const 
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:
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.  
Look up this member in the source code.  
Toggle details  bool QTransform  quadToQuadquadToQuad ( const QPolygonF &one , const QPolygonF &two , QTransform &trans ...) ( const QPolygonF &one , const QPolygonF &two , QTransform &trans ) [static] 
Creates a transformation matrix, trans, that maps a foursided polygon, one, to another foursided 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().  
Look up this member in the source code.  
Toggle details  bool QTransform  quadToSquarequadToSquare ( const QPolygonF &quad , QTransform &trans ...) ( const QPolygonF &quad , QTransform &trans ) [static] 
Creates a transformation matrix, trans, that maps a foursided 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().  
Look up this member in the source code.  
Toggle details  void QTransform  resetreset () () 
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.  
Look up this member in the source code.  
Toggle details  QTransform & QTransform  rotaterotate ( qreal angle , Qt::Axis axis=Qt::ZAxis ...) ( qreal angle , 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 yaxis points downwards. The angle is specified in degrees. See also setMatrix().  
Look up this member in the source code.  
Toggle details  QTransform & QTransform  rotateRadiansrotateRadians ( qreal angle , Qt::Axis axis=Qt::ZAxis ...) ( qreal angle , 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 yaxis points downwards. The angle is specified in radians. See also setMatrix().  
Look up this member in the source code.  
Toggle details  QTransform & QTransform  scalescale ( qreal sx , qreal sy ) ( qreal sx , qreal sy ) 
Scales the coordinate system by sx horizontally and sy vertically, and returns a reference to the matrix. See also setMatrix().  
Look up this member in the source code.  
Toggle details  void QTransform  setMatrixsetMatrix ( qreal m11 , qreal m12 , qreal m13 , qreal m21 , qreal m22 , qreal m23 , qreal m31 , qreal m32 , qreal m33 ...) ( qreal m11 , qreal m12 , qreal m13 , qreal m21 , qreal m22 , qreal m23 , qreal m31 , qreal m32 , qreal m33 ) 
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().  
Look up this member in the source code.  
Toggle details  QTransform & QTransform  shearshear ( qreal sh , qreal sv ) ( qreal sh , qreal sv ) 
Shears the coordinate system by sh horizontally and sv vertically, and returns a reference to the matrix. See also setMatrix().  
Look up this member in the source code.  
Toggle details  bool QTransform  squareToQuadsquareToQuad ( const QPolygonF &quad , QTransform &trans ...) ( const QPolygonF &quad , QTransform &trans ) [static] 
Creates a transformation matrix, trans, that maps a unit square to a foursided polygon, quad. Returns true if the transformation is constructed or false if such a transformation does not exist. See also quadToSquare() and quadToQuad().  
Look up this member in the source code.  
Toggle details  const QMatrix & QTransform  toAffinetoAffine () ()const 
Returns the QTransform as an affine matrix. Warning: If a perspective transformation has been specified, then the conversion will cause loss of data.  
Look up this member in the source code.  
Toggle details  QTransform & QTransform  translatetranslate ( qreal dx , qreal dy ) ( qreal dx , qreal 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().  
Look up this member in the source code.  
Toggle details  QTransform QTransform  transposedtransposed () ()const 
Returns the transpose of this matrix.  
Look up this member in the source code.  
Toggle details  TransformationType QTransform  typetype () ()const 
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.  
Look up this member in the source code.  
Toggle details  QTransform  operator QVariantoperator QVariant () ()const 
Returns the transform as a QVariant.  
Look up this member in the source code.  
Toggle details  bool QTransform  operator!=operator!= ( const QTransform &matrix ) ( const QTransform &matrix )const 
Returns true if this matrix is not equal to the given matrix, otherwise returns false.  
Look up this member in the source code.  
Toggle details  QTransform QTransform  operator*operator* ( const QTransform &matrix ) ( const QTransform &matrix )const 
Returns the result of multiplying this matrix by the given matrix. Note that matrix multiplication is not commutative, i.e. a*b != b*a.  
Look up this member in the source code.  
Toggle details  QTransform & QTransform  operator*=operator*= ( const QTransform &matrix ) ( const QTransform &matrix ) 
This is an overloaded function. Returns the result of multiplying this matrix by the given matrix.  
Look up this member in the source code.  
Toggle details  QTransform & QTransform  operator*=operator*= ( qreal scalar ) ( qreal scalar ) 
This is an overloaded function. Returns the result of performing an elementwise multiplication of this matrix with the given scalar.  
Look up this member in the source code.  
Toggle details  QTransform & QTransform  operator+=operator+= ( qreal scalar ) ( qreal scalar ) 
This is an overloaded function. Returns the matrix obtained by adding the given scalar to each element of this matrix.  
Look up this member in the source code.  
Toggle details  QTransform & QTransform  operator=operator= ( qreal scalar ) ( qreal scalar ) 
This is an overloaded function. Returns the matrix obtained by subtracting the given scalar from each element of this matrix.  
Look up this member in the source code.  
Toggle details  QTransform & QTransform  operator/=operator/= ( qreal scalar ) ( qreal scalar ) 
This is an overloaded function. Returns the result of performing an elementwise division of this matrix by the given scalar.  
Look up this member in the source code.  
Toggle details  QTransform & QTransform  operator=operator= ( const QTransform &matrix ) ( const QTransform &matrix ) 
Assigns the given matrix's values to this matrix.  
Look up this member in the source code.  
Toggle details  bool QTransform  operator==operator== ( const QTransform &matrix ) ( const QTransform &matrix )const 
Returns true if this matrix is equal to the given matrix, otherwise returns false.  
Look up this member in the source code.  
Toggle details  qreal QTransform  detdet () ()const 
Returns the matrix's determinant. Use determinant() instead.  
Look up this member in the source code. 
No notes