QTransform 类

QTransform 类指定坐标系统的 2D 变换。 更多...

Header: #include <QTransform>
CMake: find_package(Qt6 COMPONENTS Gui REQUIRED)
target_link_libraries(mytarget PRIVATE Qt6::Gui)
qmake: QT += gui

公共类型

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

公共函数

QTransform (qreal m11 , qreal m12 , qreal m21 , qreal m22 , qreal dx , qreal dy )
QTransform (qreal m11 , qreal m12 , qreal m13 , qreal m21 , qreal m22 , qreal m23 , qreal m31 , qreal m32 , qreal m33 )
QTransform ()
QTransform & operator= (const QTransform & matrix )
qreal m11 () const
qreal m12 () const
qreal m13 () const
qreal m21 () const
qreal m22 () const
qreal m23 () const
qreal m31 () const
qreal m32 () const
qreal m33 () const
QTransform adjoint () const
qreal determinant () const
qreal dx () const
qreal dy () const
QTransform inverted (bool * invertible = nullptr) const
bool isAffine () const
bool isIdentity () const
bool isInvertible () const
bool isRotating () const
bool isScaling () const
bool isTranslating () const
void map (qreal x , qreal y , qreal * tx , qreal * ty ) const
QPoint map (const QPoint & point ) const
QPointF map (const QPointF & p ) const
QLine map (const QLine & l ) 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
void map (int x , int y , int * tx , int * ty ) const
QRectF mapRect (const QRectF & rectangle ) const
QRect mapRect (const QRect & rectangle ) const
QPolygon mapToPolygon (const QRect & rectangle ) const
void reset ()
QTransform & rotate (qreal angle , Qt::Axis axis = Qt::ZAxis)
QTransform & rotateRadians (qreal angle , Qt::Axis axis = Qt::ZAxis)
QTransform & scale (qreal sx , qreal sy )
void setMatrix (qreal m11 , qreal m12 , qreal m13 , qreal m21 , qreal m22 , qreal m23 , qreal m31 , qreal m32 , qreal m33 )
QTransform & shear (qreal sh , qreal sv )
QTransform & translate (qreal dx , qreal dy )
QTransform transposed () const
QTransform::TransformationType type () const
QVariant operator QVariant () const
bool operator!= (const QTransform & matrix ) const
QTransform operator* (const QTransform & matrix ) const
QTransform & operator*= (const QTransform & matrix )
QTransform & operator*= (qreal scalar )
QTransform & operator+= (qreal scalar )
QTransform & operator-= (qreal scalar )
QTransform & operator/= (qreal scalar )
bool operator== (const QTransform & matrix ) const

静态公共成员

QTransform fromScale (qreal sx , qreal sy )
QTransform fromTranslate (qreal dx , qreal dy )
bool quadToQuad (const QPolygonF & one , const QPolygonF & two , QTransform & trans )
bool quadToSquare (const QPolygonF & quad , QTransform & trans )
bool squareToQuad (const QPolygonF & quad , QTransform & trans )
bool qFuzzyCompare (const QTransform & t1 , const QTransform & t2 )
size_t qHash (const QTransform & key , size_t seed = 0)
QPoint operator* (const QPoint & point , const QTransform & matrix )
QPointF operator* (const QPointF & point , const QTransform & matrix )
QLineF operator* (const QLineF & line , const QTransform & matrix )
QLine operator* (const QLine & line , const QTransform & matrix )
QPolygonF operator* (const QPolygonF & polygon , const QTransform & matrix )
QPolygon operator* (const QPolygon & polygon , const QTransform & matrix )
QRegion operator* (const QRegion & region , const QTransform & matrix )
QPainterPath operator* (const QPainterPath & path , const QTransform & matrix )
QDataStream & operator<< (QDataStream & stream , const QTransform & matrix )
QDataStream & operator>> (QDataStream & stream , QTransform & matrix )

详细描述

A transformation specifies how to translate, scale, shear, rotate or project the coordinate system, and is typically used when rendering graphics.

A QTransform object can be built using the setMatrix (), scale (), rotate (), translate () 和 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 () 函数。

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 () 函数。

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.

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 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");
}
										

基本矩阵运算

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 () 和 shear () convenience functions. The currently set values can be retrieved using the m11 (), m12 (), m13 (), m21 (), m22 (), m23 (), m31 (), m32 (), m33 (), 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 , m22 ,和 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");
}
										

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

成员类型文档编制

enum QTransform:: TransformationType

常量
QTransform::TxNone 0x00
QTransform::TxTranslate 0x01
QTransform::TxScale 0x02
QTransform::TxRotate 0x04
QTransform::TxShear 0x08
QTransform::TxProject 0x10

成员函数文档编制

QTransform:: QTransform ( 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 ().

QTransform:: QTransform ( qreal m11 , qreal m12 , qreal m13 , qreal m21 , qreal m22 , qreal m23 , qreal m31 , qreal m32 , qreal m33 )

构造矩阵采用元素 m11 , m12 , m13 , m21 , m22 , m23 , m31 , m32 , m33 .

另请参阅 setMatrix ().

QTransform:: QTransform ()

构造恒等矩阵。

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

另请参阅 reset ().

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

赋值给定 matrix 's values to this matrix.

qreal QTransform:: m11 () const

Returns the horizontal scaling factor.

另请参阅 scale () 和 基本矩阵运算 .

qreal QTransform:: m12 () const

Returns the vertical shearing factor.

另请参阅 shear () 和 基本矩阵运算 .

qreal QTransform:: m13 () const

Returns the horizontal projection factor.

另请参阅 translate () 和 基本矩阵运算 .

qreal QTransform:: m21 () const

Returns the horizontal shearing factor.

另请参阅 shear () 和 基本矩阵运算 .

qreal QTransform:: m22 () const

Returns the vertical scaling factor.

另请参阅 scale () 和 基本矩阵运算 .

qreal QTransform:: m23 () const

Returns the vertical projection factor.

另请参阅 translate () 和 基本矩阵运算 .

qreal QTransform:: m31 () const

Returns the horizontal translation factor.

另请参阅 dx (), translate (),和 基本矩阵运算 .

qreal QTransform:: m32 () const

Returns the vertical translation factor.

另请参阅 dy (), translate (),和 基本矩阵运算 .

qreal QTransform:: m33 () const

Returns the division factor.

另请参阅 translate () 和 基本矩阵运算 .

QTransform QTransform:: adjoint () const

Returns the adjoint of this matrix.

qreal QTransform:: determinant () const

Returns the matrix's determinant.

qreal QTransform:: dx () const

Returns the horizontal translation factor.

另请参阅 m31 (), translate (),和 基本矩阵运算 .

qreal QTransform:: dy () const

Returns the vertical translation factor.

另请参阅 translate () 和 基本矩阵运算 .

[static] QTransform QTransform:: fromScale ( qreal sx , qreal sy )

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.

[static] QTransform QTransform:: fromTranslate ( qreal dx , qreal dy )

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.

QTransform QTransform:: 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.

另请参阅 isInvertible ().

bool QTransform:: isAffine () const

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

bool QTransform:: isIdentity () const

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

另请参阅 reset ().

bool QTransform:: isInvertible () const

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

另请参阅 inverted ().

bool QTransform:: isRotating () const

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

注意: A rotation transformation of 180 degrees and/or 360 degrees is treated as a scaling transformation.

另请参阅 reset ().

bool QTransform:: isScaling () const

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

另请参阅 reset ().

bool QTransform:: isTranslating () const

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

另请参阅 reset ().

void QTransform:: 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 ,分别。

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.

另请参阅 基本矩阵运算 .

QPoint QTransform:: 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 QTransform:: map (const QPointF & p ) const

这是重载函数。

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

QLine QTransform:: map (const QLine & l ) const

这是重载函数。

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

QLineF QTransform:: map (const QLineF & 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.

QPolygonF QTransform:: 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 QTransform:: 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 QTransform:: 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 QTransform:: 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.

void QTransform:: 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 and * ty , respectively. Note that the transformed coordinates are rounded to the nearest integer.

QRectF QTransform:: 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 (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 () 函数代替。

另请参阅 mapToPolygon () 和 基本矩阵运算 .

QRect QTransform:: 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 QTransform:: 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
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) .

另请参阅 mapRect () 和 基本矩阵运算 .

[static] bool QTransform:: quadToQuad (const QPolygonF & one , const QPolygonF & two , QTransform & trans )

Creates a transformation matrix, trans , that maps a four-sided polygon, one , to another four-sided polygon, two 。返回 true if the transformation is possible; otherwise returns false.

This is a convenience method combining quadToSquare () 和 squareToQuad () methods. It allows the input quad to be transformed into any other quad.

另请参阅 squareToQuad () 和 quadToSquare ().

[static] bool QTransform:: quadToSquare (const QPolygonF & quad , QTransform & trans )

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.

另请参阅 squareToQuad () 和 quadToQuad ().

void QTransform:: reset ()

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.

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

QTransform &QTransform:: rotate ( 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 y-axis points downwards.

The angle is specified in degrees.

另请参阅 setMatrix ().

QTransform &QTransform:: rotateRadians ( 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 y-axis points downwards.

The angle is specified in radians.

另请参阅 setMatrix ().

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

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

另请参阅 setMatrix ().

void QTransform:: setMatrix ( 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 () 和 shear () convenience functions to manipulate the various matrix elements based on the currently defined coordinate system.

另请参阅 QTransform ().

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

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

另请参阅 setMatrix ().

[static] bool QTransform:: squareToQuad (const QPolygonF & quad , QTransform & trans )

Creates a transformation matrix, trans , that maps a unit square to a four-sided polygon, quad 。返回 true if the transformation is constructed or false if such a transformation does not exist.

另请参阅 quadToSquare () 和 quadToQuad ().

QTransform &QTransform:: 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.

另请参阅 setMatrix ().

QTransform QTransform:: transposed () const

Returns the transpose of this matrix.

QTransform::TransformationType QTransform:: type () 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.

QVariant QTransform:: operator QVariant () const

Returns the transform as a QVariant .

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

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

QTransform QTransform:: operator* (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.

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

这是重载函数。

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

QTransform &QTransform:: operator*= ( qreal scalar )

这是重载函数。

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

QTransform &QTransform:: operator+= ( qreal scalar )

这是重载函数。

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

QTransform &QTransform:: operator-= ( qreal scalar )

这是重载函数。

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

QTransform &QTransform:: operator/= ( qreal scalar )

这是重载函数。

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

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

返回 true if this matrix is equal to the given matrix ,否则返回 false .

相关非成员

bool qFuzzyCompare (const QTransform & t1 , const QTransform & t2 )

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

[since 5.6] size_t qHash (const QTransform & key , size_t seed = 0)

返回哈希值为 key ,使用 seed 进行种子计算。

该函数在 Qt 5.6 引入。

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

这如同 matrix .map( point ).

另请参阅 QTransform::map ().

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

如同 matrix .map( point ).

另请参阅 QTransform::map ().

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

这如同 matrix .map( line ).

另请参阅 QTransform::map ().

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

这如同 matrix .map( line ).

另请参阅 QTransform::map ().

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

这如同 matrix .map( polygon ).

另请参阅 QTransform::map ().

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

这如同 matrix .map( polygon ).

另请参阅 QTransform::map ().

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

这如同 matrix .map( region ).

另请参阅 QTransform::map ().

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

这如同 matrix .map( path ).

另请参阅 QTransform::map ().

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

Reads the given matrix from the given stream 并返回流引用。

另请参阅 序列化 Qt 数据类型 .