QTransform Class

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");
}

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 (!isAffine()) {
    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.

Combining Transforms▲

void BasicOperations::paintEvent(QPaintEvent *)
{
    const double a = qDegreesToRadians(45.0);
    double sina = sin(a);
    double cosa = cos(a);

    QTransform scale(0.5, 0, 0, 1.0, 0, 0);
    QTransform rotate(cosa, sina, -sina, cosa, 0, 0);
    QTransform translate(1, 0, 0, 1, 50.0, 50.0);

    QTransform transform = scale * rotate * translate;

    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");
}

Relation to Matrix Notation▲

See also QPainter, Coordinate System, Affine Transformations Example, Transformations Example

Constructs an identity matrix.

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

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

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

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Returns the horizontal scaling factor.

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Returns the vertical shearing factor.

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Returns the horizontal projection factor.

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Returns the horizontal shearing factor.

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Returns the vertical scaling factor.

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Returns the vertical projection factor.

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Returns the horizontal translation factor.

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Returns the vertical translation factor.

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Returns the division factor.

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Returns the adjoint of this matrix.

Returns the matrix's determinant.

Returns the horizontal translation factor.

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Returns the vertical translation factor.

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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.

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.

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.

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

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

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

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

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

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

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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 (!isAffine()) {
    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.

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

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.

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.

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.

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.

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 (!isAffine()) {
    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.

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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
if (!isAffine()) {
    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).

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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.

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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.

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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.

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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.

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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.

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

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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.

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

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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.

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Moves the coordinate system dx along the x axis and dy along the y axis, and returns a reference to the matrix.

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Returns the transpose of this matrix.

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.

Returns the transform as a QVariant.

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

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

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

This is an overloaded function.

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

This is an overloaded function.

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

This is an overloaded function.

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

This is an overloaded function.

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

This is an overloaded function.

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

Assigns the given matrix's values to this matrix.

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

Returns true if t1 and t2 are equal, allowing for a small fuzziness factor for floating-point comparisons; false otherwise.

Returns the hash value for key, using seed to seed the calculation.

This function was introduced in Qt 5.6.

This is the same as matrix.map(point).

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Same as matrix.map(point).

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This is the same as matrix.map(line).

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This is the same as matrix.map(line).

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This is the same as matrix.map(polygon).

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This is the same as matrix.map(polygon).

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This is the same as matrix.map(region).

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This is the same as matrix.map(path).

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Writes the given matrix to the given stream and returns a reference to the stream.

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Reads the given matrix from the given stream and returns a reference to the stream.

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