CopperSpice API  1.7.2
QMatrix Class Reference

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

Public Methods

 QMatrix ()
 
 QMatrix (const QMatrix &other)
 
 QMatrix (qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)
 
qreal determinant () const
 
qreal dx () const
 
qreal dy () const
 
QMatrix inverted (bool *invertible=nullptr) const
 
bool isIdentity () const
 
bool isInvertible () const
 
qreal m11 () const
 
qreal m12 () const
 
qreal m21 () const
 
qreal m22 () const
 
QLine map (const QLine &l) const
 
QLineF map (const QLineF &l) const
 
QPainterPath map (const QPainterPath &p) const
 
QPoint map (const QPoint &p) const
 
QPointF map (const QPointF &p) const
 
QPolygon map (const QPolygon &a) const
 
QPolygonF map (const QPolygonF &a) const
 
QRegion map (const QRegion &r) const
 
void map (int x, int y, int *tx, int *ty) const
 
void map (qreal x, qreal y, qreal *tx, qreal *ty) const
 
QRect mapRect (const QRect &) const
 
QRectF mapRect (const QRectF &) const
 
QPolygon mapToPolygon (const QRect &r) const
 
 operator QVariant () const
 
bool operator!= (const QMatrix &matrix) const
 
QMatrix operator* (const QMatrix &matrix) const
 
QMatrix & operator*= (const QMatrix &matrix)
 
QMatrix & operator= (const QMatrix &matrix)
 
bool operator== (const QMatrix &matrix) const
 
void reset ()
 
QMatrix & rotate (qreal a)
 
QMatrix & scale (qreal sx, qreal sy)
 
void setMatrix (qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)
 
QMatrix & shear (qreal sh, qreal sv)
 
QMatrix & translate (qreal dx, qreal dy)
 

Friends

class QTransform
 

Related Functions

These are not member functions

QLine operator* (const QLine &line, const QMatrix &matrix)
 
QLineF operator* (const QLineF &line, const QMatrix &matrix)
 
QPainterPath operator* (const QPainterPath &path, const QMatrix &matrix)
 
QPoint operator* (const QPoint &point, const QMatrix &matrix)
 
QPointF operator* (const QPointF &point, const QMatrix &matrix)
 
QPolygon operator* (const QPolygon &polygon, const QMatrix &matrix)
 
QPolygonF operator* (const QPolygonF &polygon, const QMatrix &matrix)
 
QRegion operator* (const QRegion &region, const QMatrix &matrix)
 
QDataStreamoperator<< (QDataStream &stream, const QMatrix &matrix)
 
QDataStreamoperator>> (QDataStream &stream, QMatrix &matrix)
 
bool qFuzzyCompare (const QMatrix &m1, const QMatrix &m2)
 

Detailed Description

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 CopperSpice.

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.

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 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");
}

Basic Matrix Operations

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 is the combined transformations example using basic matrix operations:

void BasicOperations::paintEvent(QPaintEvent *)
{
double pi = 3.14;
double angle = pi/180 * 45.0;
double sinAngle = sin(angle);
double cosAngle = cos(angle);
QMatrix translationMatrix(1, 0, 0, 1, 50.0, 50.0);
QMatrix rotationMatrix(cosAngle, sinAngle, -sinAngle, cosAngle, 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");
}
See also
QPainter, QTransform, Coordinate System

Constructor & Destructor Documentation

QMatrix::QMatrix ( )

Constructs an identity matrix.

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

See also
reset()
QMatrix::QMatrix ( 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()
QMatrix::QMatrix ( const QMatrix &  other)

Copy constructs a new QMatrix from other.

Method Documentation

qreal QMatrix::determinant ( ) const
inline

Returns the matrix's determinant.

qreal QMatrix::dx ( ) const
inline

Returns the horizontal translation factor.

See also
translate(), Basic Matrix Operations
qreal QMatrix::dy ( ) const
inline

Returns the vertical translation factor.

See also
translate(), Basic Matrix Operations
QMatrix QMatrix::inverted ( bool *  invertible = nullptr) 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()
bool QMatrix::isIdentity ( ) const
inline

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

See also
reset()
bool QMatrix::isInvertible ( ) const
inline

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

See also
inverted()
qreal QMatrix::m11 ( ) const
inline

Returns the horizontal scaling factor.

See also
scale(), Basic Matrix Operations
qreal QMatrix::m12 ( ) const
inline

Returns the vertical shearing factor.

See also
shear(), Basic Matrix Operations
qreal QMatrix::m21 ( ) const
inline

Returns the horizontal shearing factor.

See also
shear(), Basic Matrix Operations
qreal QMatrix::m22 ( ) const
inline

Returns the vertical scaling factor.

See also
scale(), Basic Matrix Operations
QLine QMatrix::map ( const QLine line) const

Creates and returns a QLine object that is a copy of the given line, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QLineF QMatrix::map ( const QLineF line) const

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

QPainterPath QMatrix::map ( const QPainterPath path) const

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

QPoint QMatrix::map ( const QPoint point) const

Creates and returns a QPoint object that is a copy of the given point, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QPointF QMatrix::map ( const QPointF point) const

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

QPolygon QMatrix::map ( const QPolygon polygon) const

Creates and returns a QPolygon object that is a copy of the given polygon, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QPolygonF QMatrix::map ( const QPolygonF polygon) const

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

QRegion QMatrix::map ( const QRegion region) const

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.

void QMatrix::map ( int  x,
int  y,
int *  tx,
int *  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 transformed coordinates are rounded to the nearest integer.

void QMatrix::map ( 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:

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
QRect QMatrix::mapRect ( const QRect rectangle) const

Creates and returns a QRect object that is a copy of the given rectangle, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QRectF QMatrix::mapRect ( 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:

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(), Basic Matrix Operations
QPolygon QMatrix::mapToPolygon ( 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:

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(), Basic Matrix Operations
QMatrix::operator QVariant ( ) const

Returns the matrix as a QVariant.

bool QMatrix::operator!= ( const QMatrix &  matrix) const

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

QMatrix QMatrix::operator* ( const QMatrix &  matrix) const

Returns the result of multiplying this matrix by the given matrix. The matrix multiplication is not commutative, for example: a*b != b*a.

QMatrix & QMatrix::operator*= ( const QMatrix &  matrix)

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

QMatrix & QMatrix::operator= ( const QMatrix &  matrix)

Assigns the given matrix's values to this matrix.

bool QMatrix::operator== ( const QMatrix &  matrix) const

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

void QMatrix::reset ( )

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

See also
QMatrix(), isIdentity(), Basic Matrix Operations
QMatrix & QMatrix::rotate ( qreal  degrees)

Rotates the coordinate system the given degrees counterclockwise.

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()
QMatrix & QMatrix::scale ( qreal  sx,
qreal  sy 
)

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

See also
setMatrix()
void QMatrix::setMatrix ( qreal  m11,
qreal  m12,
qreal  m21,
qreal  m22,
qreal  dx,
qreal  dy 
)

Sets the matrix elements to the specified values, m11, m12, m21, m22, dx and dy.

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()
QMatrix & QMatrix::shear ( qreal  sh,
qreal  sv 
)

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

See also
setMatrix()
QMatrix & QMatrix::translate ( 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()

Friends And Related Function Documentation

QLine operator* ( const QLine line,
const QMatrix &  matrix 
)
related

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

See also
QMatrix::map()
QLineF operator* ( const QLineF line,
const QMatrix &  matrix 
)
related

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

See also
QMatrix::map()
QPainterPath operator* ( const QPainterPath path,
const QMatrix &  matrix 
)
related

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

See also
QMatrix::map()
QPoint operator* ( const QPoint point,
const QMatrix &  matrix 
)
related

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

See also
QMatrix::map()
QPointF operator* ( const QPointF point,
const QMatrix &  matrix 
)
related

Same as matrix.map(point).

See also
QMatrix::map()
QPolygon operator* ( const QPolygon polygon,
const QMatrix &  matrix 
)
related

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

See also
QMatrix::map()
QPolygonF operator* ( const QPolygonF polygon,
const QMatrix &  matrix 
)
related

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

See also
QMatrix::map()
QRegion operator* ( const QRegion region,
const QMatrix &  matrix 
)
related

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

See also
QMatrix::map()
QDataStream & operator<< ( QDataStream stream,
const QMatrix &  matrix 
)
related

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

See also
Refer to Serializing Data Types for additional information
QDataStream & operator>> ( QDataStream stream,
QMatrix &  matrix 
)
related

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

See also
Refer to Serializing Data Types for additional information
bool qFuzzyCompare ( const QMatrix &  m1,
const QMatrix &  m2 
)
related

The qFuzzyCompare function is for comparing two matrices using a fuzziness factor.

Returns true if m1 and m2 are equal, allowing for a small fuzziness factor for floating-point comparisons; false otherwise.