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QMatrix Class

QMatrix class specifies 2D transformations of a coordinate system. 更多...

头： #include <QMatrix>
qmake: QT += gui

该类已过时。 提供它是为使旧源代码能继续工作。强烈建议不要在新代码中使用它。

公共函数

QMatrix ()
QMatrix (qreal m11 , qreal m12 , qreal m21 , qreal m22 , qreal dx , qreal dy )
QMatrix (QMatrix && other )
QMatrix (const QMatrix & matrix )
qreal m11 () const
qreal m12 () const
qreal m21 () const
qreal m22 () const
qreal determinant () const
qreal dx () const
qreal dy () const
QMatrix inverted (bool * invertible = Q_NULLPTR) const
bool isIdentity () const
bool isInvertible () const
void map (qreal x , qreal y , qreal * tx , qreal * ty ) const
void map (int x , int y , int * tx , int * ty ) const
QPoint map (const QPoint & point ) const
QPointF map (const QPointF & point ) const
QLine map (const QLine & line ) const
QLineF map (const QLineF & line ) const
QPolygonF map (const QPolygonF & polygon ) const
QPolygon map (const QPolygon & polygon ) const
QRegion map (const QRegion & region ) const
QPainterPath map (const QPainterPath & path ) const
QRectF mapRect (const QRectF & rectangle ) const
QRect mapRect (const QRect & rectangle ) const
QPolygon mapToPolygon (const QRect & rectangle ) const
void reset ()
QMatrix & rotate (qreal degrees )
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 )
operator QVariant () const
bool operator!= (const QMatrix & matrix ) const
QMatrix operator* (const QMatrix & matrix ) const
QMatrix & operator*= (const QMatrix & matrix )
QMatrix & operator= (QMatrix && other )
QMatrix & operator= (const QMatrix & matrix )
bool operator== (const QMatrix & matrix ) const
bool qFuzzyCompare (const QMatrix & m1 , const QMatrix & m2 )
uint qHash (const QMatrix & key , uint seed = 0)
QPoint operator* (const QPoint & point , const QMatrix & matrix )
QPointF operator* (const QPointF & point , const QMatrix & matrix )
QLineF operator* (const QLineF & line , const QMatrix & matrix )
QLine operator* (const QLine & line , const QMatrix & matrix )
QPolygonF operator* (const QPolygonF & polygon , const QMatrix & matrix )
QPolygon operator* (const QPolygon & polygon , const QMatrix & matrix )
QRegion operator* (const QRegion & region , const QMatrix & matrix )
QPainterPath operator* (const QPainterPath & path , const QMatrix & matrix )
QDataStream & operator<< (QDataStream & stream , const QMatrix & matrix )
QDataStream & operator>> (QDataStream & stream , QMatrix & matrix )

详细描述

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 Qt.

A QMatrix object can be built using the setMatrix (), scale (), rotate (), translate () 和 shear () 函数。另外，可以构建它通过应用 基本矩阵运算 。矩阵也可以在构造时定义，且可以把它重置为恒等矩阵 (默认) 使用 reset () 函数。

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 () 函数。

QMatrix 提供 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 提供 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.

渲染图形

When rendering graphics, the matrix defines the transformations but the actual transformation is performed by the drawing routines in QPainter .

默认情况下， 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 文档编制。

QPainter has functions to translate, scale, shear and rotate the coordinate system without using a QMatrix 。例如： 

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 和调用 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");
}

基本矩阵运算

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

点 (x, y) 是原点，和 (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 () 和 shear () convenience functions, The currently set values can be retrieved using the m11 (), m12 (), m21 (), m22 (), dx () 和 dy () 函数。

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'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);
    QMatrix translationMatrix(1, 0, 0, 1, 50.0, 50.0);
    QMatrix rotationMatrix(cosa, sina, -sina, cosa, 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");
}

另请参阅 QPainter , QTransform , 坐标系 , 仿射变换范例 ，和 变换范例 .

成员函数文档编制

QMatrix:: QMatrix ()

构造恒等矩阵。

所有元素被设为 0 除了 m11 and m22 (specifying the scale), which are set to 1.

另请参阅 reset ().

QMatrix:: QMatrix ( qreal m11 , qreal m12 , qreal m21 , qreal m22 , qreal dx , qreal dy )

构造矩阵采用元素 m11 , m12 , m21 , m22 , dx and dy .

另请参阅 setMatrix ().

QMatrix:: QMatrix ( QMatrix && other )

移动拷贝构造函数。

QMatrix:: QMatrix (const QMatrix & matrix )

Constructs a matrix that is a copy of the given matrix .

qreal QMatrix:: m11 () const

Returns the horizontal scaling factor.

另请参阅 scale () 和 基本矩阵运算 .

qreal QMatrix:: m12 () const

Returns the vertical shearing factor.

另请参阅 shear () 和 基本矩阵运算 .

qreal QMatrix:: m21 () const

Returns the horizontal shearing factor.

另请参阅 shear () 和 基本矩阵运算 .

qreal QMatrix:: m22 () const

Returns the vertical scaling factor.

另请参阅 scale () 和 基本矩阵运算 .

qreal QMatrix:: determinant () const

返回矩阵的行列式。

该函数在 Qt 4.6 引入。

qreal QMatrix:: dx () const

Returns the horizontal translation factor.

另请参阅 translate () 和 基本矩阵运算 .

qreal QMatrix:: dy () const

返回垂直翻译因子。

另请参阅 translate () 和 基本矩阵运算 .

QMatrix QMatrix:: inverted ( bool * invertible = Q_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.

另请参阅 isInvertible ().

bool QMatrix:: isIdentity () const

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

另请参阅 reset ().

bool QMatrix:: isInvertible () const

返回 true 若矩阵可逆，否则返回 false .

另请参阅 inverted ().

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 和 * ty ，分别。

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.

另请参阅 基本矩阵运算 .

void QMatrix:: map ( int x , int y , int * tx , int * ty ) const

这是重载函数。

Maps the given coordinates x and y into the coordinate system defined by this matrix. The resulting values are put in * tx 和 * ty , respectively. Note that the transformed coordinates are rounded to the nearest integer.

QPoint QMatrix:: map (const QPoint & point ) const

这是重载函数。

创建和返回 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 QMatrix:: map (const QPointF & point ) const

这是重载函数。

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

QLine QMatrix:: map (const QLine & line ) const

这是重载函数。

创建和返回 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 QMatrix:: map (const QLineF & line ) const

这是重载函数。

创建和返回 QLineF object that is a copy of the given line , mapped into the coordinate system defined by this matrix.

QPolygonF QMatrix:: map (const QPolygonF & polygon ) const

这是重载函数。

创建和返回 QPolygonF object that is a copy of the given polygon , mapped into the coordinate system defined by this matrix.

QPolygon QMatrix:: map (const QPolygon & polygon ) const

这是重载函数。

创建和返回 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.

QRegion QMatrix:: map (const QRegion & region ) const

这是重载函数。

创建和返回 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.

QPainterPath QMatrix:: map (const QPainterPath & path ) const

这是重载函数。

创建和返回 QPainterPath object that is a copy of the given path , mapped into the coordinate system defined by this matrix.

QRectF QMatrix:: mapRect (const QRectF & rectangle ) const

创建和返回 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 () 函数代替。

另请参阅 mapToPolygon () 和 基本矩阵运算 .

QRect QMatrix:: mapRect (const QRect & rectangle ) const

这是重载函数。

创建和返回 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 QMatrix:: mapToPolygon (const QRect & rectangle ) const

创建和返回 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) .

另请参阅 mapRect () 和 基本矩阵运算 .

void QMatrix:: reset ()

将矩阵重置为恒等矩阵，即，所有元素被设为 0，除了 m11 and m22 (specifying the scale) which are set to 1.

另请参阅 QMatrix (), isIdentity ()，和 基本矩阵运算 .

QMatrix &QMatrix:: rotate ( qreal degrees )

Rotates the coordinate system the given degrees counterclockwise.

注意，若应用 QMatrix 到由 Widget 坐标定义的点，旋转方向将是顺时针，因为 Y 轴指向向下。

Returns a reference to the matrix.

另请参阅 setMatrix ().

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

比例缩放坐标系按 sx 水平和 sy 垂直，并返回矩阵引用。

另请参阅 setMatrix ().

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

将矩阵元素设为指定值， m11 , m12 , m21 , m22 , dx and dy .

Note that this function replaces the previous values. QMatrix provide the translate (), rotate (), scale () 和 shear () convenience functions to manipulate the various matrix elements based on the currently defined coordinate system.

另请参阅 QMatrix ().

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

剪切坐标系按 sh 水平和 sv 垂直，并返回矩阵引用。

另请参阅 setMatrix ().

QMatrix &QMatrix:: translate ( qreal dx , qreal dy )

移动坐标系 dx 沿 X 轴和 dy 沿 Y 轴，并返回矩阵引用。

另请参阅 setMatrix ().

QMatrix:: operator QVariant () const

Returns the matrix as a QVariant .

该函数在 Qt 4.2 引入。

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

返回 true if this matrix is not equal to the given matrix ，否则返回 false .

QMatrix QMatrix:: operator* (const QMatrix & 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.

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

这是重载函数。

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

QMatrix &QMatrix:: operator= ( QMatrix && other )

移动赋值运算符。

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

赋值给定 matrix 的值到此矩阵。

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

返回 true 若此矩阵等于给定 matrix ，否则返回 false .

相关非成员

bool qFuzzyCompare (const QMatrix & m1 , const QMatrix & m2 )

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

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

该函数在 Qt 4.6 引入。

uint qHash (const QMatrix & key , uint seed = 0)

返回哈希值为 key ，使用 seed 做计算种子。

该函数在 Qt 5.6 引入。

QPoint operator* (const QPoint & point , const QMatrix & matrix )

这如同 matrix .map( point ).

另请参阅 QMatrix::map ().

QPointF operator* (const QPointF & point , const QMatrix & matrix )

如同 matrix .map( point ).

另请参阅 QMatrix::map ().

QLineF operator* (const QLineF & line , const QMatrix & matrix )

这如同 matrix .map( line ).

另请参阅 QMatrix::map ().

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

这如同 matrix .map( line ).

另请参阅 QMatrix::map ().

QPolygonF operator* (const QPolygonF & polygon , const QMatrix & matrix )

这如同 matrix .map( polygon ).

另请参阅 QMatrix::map ().

QPolygon operator* (const QPolygon & polygon , const QMatrix & matrix )

这如同 matrix .map( polygon ).

另请参阅 QMatrix::map ().

QRegion operator* (const QRegion & region , const QMatrix & matrix )

这如同 matrix .map( region ).

另请参阅 QMatrix::map ().

QPainterPath operator* (const QPainterPath & path , const QMatrix & matrix )

这如同 matrix .map( path ).

另请参阅 QMatrix::map ().

QDataStream & operator<< ( QDataStream & stream , const QMatrix & matrix )

写入给定 matrix 到给定 stream 并返回流引用。

另请参阅 序列化 Qt 数据类型 .

QDataStream & operator>> ( QDataStream & stream , QMatrix & matrix )

读取给定 matrix 从给定 stream 并返回流引用。

另请参阅 序列化 Qt 数据类型 .