QTransform 类指定坐标系的 2D 变换。 更多...
| 头： | #include <QTransform> |
| CMake: |
find_package(Qt6 REQUIRED COMPONENTS Gui)
target_link_libraries(mytarget PRIVATE Qt6::Gui) |
| qmake: | QT += gui |
| enum | TransformationType { TxNone, TxTranslate, TxScale, TxRotate, TxShear, TxProject } |
| QTransform () | |
| QTransform (qreal m11 , qreal m12 , qreal m13 , qreal m21 , qreal m22 , qreal m23 , qreal m31 , qreal m32 , qreal m33 ) | |
| QTransform (qreal m11 , qreal m12 , qreal m21 , qreal m22 , qreal dx , qreal dy ) | |
| 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 a , Qt::Axis axis , qreal distanceToPlane ) |
| QTransform & | rotate (qreal a , Qt::Axis axis = Qt::ZAxis) |
| QTransform & | rotateRadians (qreal a , Qt::Axis axis , qreal distanceToPlane ) |
| QTransform & | rotateRadians (qreal a , 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 ) |
| QTransform & | operator= (const QTransform & matrix ) |
| bool | operator== (const QTransform & matrix ) const |
| 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 ) |
变换指定如何平移、比例缩放、剪切、旋转或投影坐标系，且通常在渲染图形时使用。
可以构建 QTransform 对象使用 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。
QTransform 类支持图形原语的映射：可以将给定点、线、多边形、区域或描绘器路径，映射到坐标系定义通过 this 矩阵使用 map () 函数。若是矩形，变换其坐标可以使用 mapRect () 函数。还可以将矩形变换成 polygon (映射到坐标系定义通过 this 矩阵)，使用 mapToPolygon () 函数。
QTransform 提供
isIdentity
() 函数其返回
true
如果矩阵是恒等矩阵，和
isInvertible
() 函数其返回
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.
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 坐标系 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"); } |
QTransform 对象包含 3 x 3 矩阵。
m31
(
dx
) 和
m32
(
dy
) 元素指定水平和垂直平移。
m11
and
m22
元素指定水平和垂直比例缩放。
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'
}
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 (), 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 *) { 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"); } |
The combined transform first scales each operand, then rotates it, and finally translates it, just as in the order in which the product of its factors is written. This means the point to which the transforms are applied is implicitly multiplied on the left with the transform to its right.
The matrix notation in QTransform is the transpose of a commonly-taught convention which represents transforms and points as matrices and vectors. That convention multiplies its matrix on the left and column vector to the right. In other words, when several transforms are applied to a point, the right-most matrix acts directly on the vector first. Then the next matrix to the left acts on the result of the first operation - and so on. As a result, that convention multiplies the matrices that make up a composite transform in the reverse of the order in QTransform, as you can see in 组合变换 . Transposing the matrices, and combining them to the right of a row vector that represents the point, lets the matrices of transforms appear, in their product, in the order in which we think of the transforms being applied to the point.
另请参阅 QPainter , 坐标系 , 仿射变换范例 ，和 变换范例 .
| 常量 | 值 |
|---|---|
QTransform::TxNone
|
0x00
|
QTransform::TxTranslate
|
0x01
|
QTransform::TxScale
|
0x02
|
QTransform::TxRotate
|
0x04
|
QTransform::TxShear
|
0x08
|
QTransform::TxProject
|
0x10
|
构造恒等矩阵。
所有元素被设为 0 除了
m11
and
m22
(指定比例) 和
m33
被设为 1。
另请参阅 reset ().
构造矩阵采用元素 m11 , m12 , m13 , m21 , m22 , m23 , m31 , m32 , m33 .
另请参阅 setMatrix ().
构造矩阵采用元素 m11 , m12 , m21 , m22 , dx and dy .
另请参阅 setMatrix ().
Returns the horizontal scaling factor.
Returns the vertical shearing factor.
Returns the horizontal projection factor.
Returns the horizontal shearing factor.
Returns the vertical scaling factor.
Returns the vertical projection factor.
Returns the horizontal translation factor.
另请参阅 dx (), translate ()，和 基本矩阵运算 .
返回垂直翻译因子。
另请参阅 dy (), translate ()，和 基本矩阵运算 .
Returns the division factor.
Returns the adjoint of this matrix.
返回矩阵的行列式。
Returns the horizontal translation factor.
另请参阅 m31 (), translate ()，和 基本矩阵运算 .
返回垂直翻译因子。
[static]
QTransform
QTransform::
fromScale
(
qreal
sx
,
qreal
sy
)
Creates a matrix which corresponds to a scaling of sx 水平和 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 沿 X 轴和 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.
另请参阅 isInvertible ().
返回
true
if the matrix represent an affine transformation, otherwise returns
false
.
返回
true
if the matrix is the identity matrix, otherwise returns
false
.
另请参阅 reset ().
返回
true
若矩阵可逆，否则返回
false
.
另请参阅 inverted ().
返回
true
若矩阵表示某种旋转变换，否则返回
false
.
注意： A rotation transformation of 180 degrees and/or 360 degrees is treated as a scaling transformation.
另请参阅 reset ().
返回
true
若矩阵表示比例缩放变换，否则返回
false
.
另请参阅 reset ().
返回
true
若矩阵表示平移变换，否则返回
false
.
另请参阅 reset ().
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
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.
另请参阅 基本矩阵运算 .
这是重载函数。
创建并返回 QPoint 副本对象为给定 point , mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.
这是重载函数。
创建并返回 QPointF object that is a copy of the given point, p , mapped into the coordinate system defined by this matrix.
这是重载函数。
创建并返回 QLineF object that is a copy of the given line, l , mapped into the coordinate system defined by this matrix.
这是重载函数。
创建并返回 QLine 副本对象为给定 line , mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.
这是重载函数。
创建并返回 QPolygonF 副本对象为给定 polygon , mapped into the coordinate system defined by this matrix.
这是重载函数。
创建并返回 QPolygon 副本对象为给定 polygon , mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.
这是重载函数。
创建并返回 QRegion 副本对象为给定 region , mapped into the coordinate system defined by this matrix.
Calling this method can be rather expensive if rotations or shearing are used.
这是重载函数。
创建并返回 QPainterPath 副本对象为给定 path , mapped into the coordinate system defined by this matrix.
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.
创建并返回 QRectF 副本对象为给定 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 () 函数代替。
另请参阅 mapToPolygon () 和 基本矩阵运算 .
这是重载函数。
创建并返回 QRect 副本对象为给定 rectangle , mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.
创建并返回 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 (!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)
.
[static]
bool
QTransform::
quadToQuad
(const
QPolygonF
&
one
, const
QPolygonF
&
two
,
QTransform
&
trans
)
创建变换矩阵
trans
，映射 4 边多边形
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
)
创建变换矩阵
trans
，映射 4 边多边形
quad
，到单位正方形。返回
true
if the transformation is constructed or false if such a transformation does not exist.
另请参阅 squareToQuad () 和 quadToQuad ().
将矩阵重置为恒等矩阵，即，所有元素被设为 0，除了
m11
and
m22
(指定比例) 和
m33
被设为 1。
另请参阅 QTransform (), isIdentity ()，和 基本矩阵运算 .
[since 6.5]
QTransform
&QTransform::
rotate
(
qreal
a
,
Qt::Axis
axis
,
qreal
distanceToPlane
)
Rotates the coordinate system counterclockwise by the given angle a 关于指定 axis at distance distanceToPlane from the screen and returns a reference to the matrix.
注意，若应用 QTransform 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。
The angle is specified in degrees. If distanceToPlane is zero, it will be ignored. This is suitable for implementing orthographic projections where the z coordinate should be dropped rather than projected.
该函数在 Qt 6.5 引入。
另请参阅 setMatrix ().
这是重载函数。
Rotates the coordinate system counterclockwise by the given angle a 关于指定 axis at distance 1024.0 from the screen and returns a reference to the matrix.
注意，若应用 QTransform 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。
角度的指定是以度为单位。
另请参阅 setMatrix .
[since 6.5]
QTransform
&QTransform::
rotateRadians
(
qreal
a
,
Qt::Axis
axis
,
qreal
distanceToPlane
)
Rotates the coordinate system counterclockwise by the given angle a 关于指定 axis at distance distanceToPlane from the screen and returns a reference to the matrix.
注意，若应用 QTransform 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。
The angle is specified in radians. If distanceToPlane is zero, it will be ignored. This is suitable for implementing orthographic projections where the z coordinate should be dropped rather than projected.
该函数在 Qt 6.5 引入。
另请参阅 setMatrix ().
这是重载函数。
Rotates the coordinate system counterclockwise by the given angle a 关于指定 axis at distance 1024.0 from the screen and returns a reference to the matrix.
注意，若应用 QTransform 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。
角度的指定是以弧度为单位。
另请参阅 setMatrix ().
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 ().
将矩阵元素设为指定值， m11 , m12 , m13 m21 , m22 , m23 m31 , m32 and m33 。注意，此函数替换先前值。 QTransform 提供 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 ().
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 ().
[static]
bool
QTransform::
squareToQuad
(const
QPolygonF
&
quad
,
QTransform
&
trans
)
创建变换矩阵
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 ().
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 ().
返回此矩阵的转置。
返回此矩阵的变换类型。
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
，因为
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.
返回变换如 QVariant .
返回
true
if this matrix is not equal to the given
matrix
，否则返回
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.
这是重载函数。
Returns the result of multiplying this matrix by the given matrix .
这是重载函数。
Returns the result of performing an element-wise multiplication of this matrix with the given scalar .
这是重载函数。
Returns the matrix obtained by adding the given scalar to each element of this matrix.
这是重载函数。
Returns the matrix obtained by subtracting the given scalar from each element of this matrix.
这是重载函数。
Returns the result of performing an element-wise division of this matrix by the given scalar .
赋值给定 matrix 的值到此矩阵。
返回
true
若此矩阵等于给定
matrix
，否则返回
false
.
返回
true
if
t1
and
t2
are equal, allowing for a small fuzziness factor for floating-point comparisons; false otherwise.
返回哈希值为 key ，使用 seed 做计算种子。
这如同 matrix .map( point ).
另请参阅 QTransform::map ().
如同 matrix .map( point ).
另请参阅 QTransform::map ().
这如同 matrix .map( line ).
另请参阅 QTransform::map ().
这如同 matrix .map( line ).
另请参阅 QTransform::map ().
这如同 matrix .map( polygon ).
另请参阅 QTransform::map ().
这如同 matrix .map( polygon ).
另请参阅 QTransform::map ().
这如同 matrix .map( region ).
另请参阅 QTransform::map ().
这如同 matrix .map( path ).
另请参阅 QTransform::map ().
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 .
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 .