QTransform¶
The QTransform
class specifies 2D transformations of a coordinate system. More…
Synopsis¶
Functions¶
def
__add__
(n)def
__div__
(n)def
__eq__
(arg__1)def
__iadd__
(div)def
__idiv__
(div)def
__imul__
(arg__1)def
__imul__
(div)def
__isub__
(div)def
__mul__
(n)def
__mul__
(o)def
__ne__
(arg__1)def
__reduce__
()def
__repr__
()def
__sub__
(n)def
adjoint
()def
determinant
()def
dx
()def
dy
()def
inverted
()def
isAffine
()def
isIdentity
()def
isInvertible
()def
isRotating
()def
isScaling
()def
isTranslating
()def
m11
()def
m12
()def
m13
()def
m21
()def
m22
()def
m23
()def
m31
()def
m32
()def
m33
()def
map
(a)def
map
(a)def
map
(l)def
map
(l)def
map
(p)def
map
(p)def
map
(p)def
map
(r)def
map
(x, y)def
mapRect
(arg__1)def
mapRect
(arg__1)def
mapToPolygon
(r)def
reset
()def
rotate
(a[, axis=Qt.ZAxis])def
rotateRadians
(a[, axis=Qt.ZAxis])def
scale
(sx, sy)def
setMatrix
(m11, m12, m13, m21, m22, m23, m31, m32, m33)def
shear
(sh, sv)def
translate
(dx, dy)def
transposed
()def
type
()
Static functions¶
def
fromScale
(dx, dy)def
fromTranslate
(dx, dy)def
quadToQuad
(arg__1, arg__2)def
quadToQuad
(one, two, result)def
quadToSquare
(arg__1)def
quadToSquare
(quad, result)def
squareToQuad
(arg__1)def
squareToQuad
(square, result)
Detailed Description¶
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()
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 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()
function.
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.
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 QTransform
. For example:
def paintEvent(self, arg__0): painter = QPainter(self) 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 setTransform()
if you want to perform more than a single transform operation. For example:
def paintEvent(self, arg__0): painter = QPainter(self) painter.setPen(QPen(Qt.blue, 1, Qt.DashLine)) painter.drawRect(0, 0, 100, 100) transform = QTransform() 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")
Basic Matrix Operations¶
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' = m11x + m21y + dx y' = m22y + m12x + dy if not isAffine(): w' = m13x + m23y + 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¶
Here’s the combined transformations example using basic matrix operations:
def paintEvent(self, arg__0): a = qDegreesToRadians(45.0) sina = sin(a) cosa = cos(a) scale = QTransform(0.5, 0, 0, 1.0, 0, 0) rotate = QTransform(cosa, sina, -sina, cosa, 0, 0) translate = QTransform(1, 0, 0, 1, 50.0, 50.0) transform = scale * rotate * translate painter = QPainter(self) 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.
Relation to Matrix Notation¶
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 Combining Transforms
. 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.
- class PySide6.QtGui.QTransform¶
PySide6.QtGui.QTransform(other)
PySide6.QtGui.QTransform(h11, h12, h13, h21, h22, h23, h31, h32, h33)
PySide6.QtGui.QTransform(h11, h12, h21, h22, dx, dy)
- Parameters
other –
PySide6.QtGui.QTransform
h22 – float
h23 – float
h21 – float
dy – float
h13 – float
h31 – float
h32 – float
dx – float
h11 – float
h33 – float
h12 – float
Constructs an identity matrix.
All elements are set to zero except m11
and m22
(specifying the scale) and m33
which are set to 1.
See also
Constructs a matrix with the elements, m11
, m12
, m13
, m21
, m22
, m23
, m31
, m32
, m33
.
See also
Constructs a matrix with the elements, m11
, m12
, m21
, m22
, dx
and dy
.
See also
- PySide6.QtGui.QTransform.TransformationType¶
Constant
Description
QTransform.TxNone
QTransform.TxTranslate
QTransform.TxScale
QTransform.TxRotate
QTransform.TxShear
QTransform.TxProject
- PySide6.QtGui.QTransform.__reduce__()¶
- Return type
object
- PySide6.QtGui.QTransform.__repr__()¶
- Return type
object
- PySide6.QtGui.QTransform.adjoint()¶
- Return type
Returns the adjoint of this matrix.
- PySide6.QtGui.QTransform.determinant()¶
- Return type
float
Returns the matrix’s determinant.
- PySide6.QtGui.QTransform.dx()¶
- Return type
float
Returns the horizontal translation factor.
See also
m31()
translate()
Basic Matrix Operations
- PySide6.QtGui.QTransform.dy()¶
- Return type
float
Returns the vertical translation factor.
See also
translate()
Basic Matrix Operations
- static PySide6.QtGui.QTransform.fromScale(dx, dy)¶
- Parameters
dx – float
dy – float
- Return type
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 PySide6.QtGui.QTransform.fromTranslate(dx, dy)¶
- Parameters
dx – float
dy – float
- Return type
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.
- PySide6.QtGui.QTransform.inverted()¶
- Return type
PyTuple
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
- PySide6.QtGui.QTransform.isAffine()¶
- Return type
bool
Returns true
if the matrix represent an affine transformation, otherwise returns false
.
- PySide6.QtGui.QTransform.isIdentity()¶
- Return type
bool
Returns true
if the matrix is the identity matrix, otherwise returns false
.
See also
- PySide6.QtGui.QTransform.isInvertible()¶
- Return type
bool
Returns true
if the matrix is invertible, otherwise returns false
.
See also
- PySide6.QtGui.QTransform.isRotating()¶
- Return type
bool
Returns true
if the matrix represents some kind of a rotating transformation, otherwise returns false
.
Note
A rotation transformation of 180 degrees and/or 360 degrees is treated as a scaling transformation.
See also
- PySide6.QtGui.QTransform.isScaling()¶
- Return type
bool
Returns true
if the matrix represents a scaling transformation, otherwise returns false
.
See also
- PySide6.QtGui.QTransform.isTranslating()¶
- Return type
bool
Returns true
if the matrix represents a translating transformation, otherwise returns false
.
See also
- PySide6.QtGui.QTransform.m11()¶
- Return type
float
Returns the horizontal scaling factor.
See also
scale()
Basic Matrix Operations
- PySide6.QtGui.QTransform.m12()¶
- Return type
float
Returns the vertical shearing factor.
See also
shear()
Basic Matrix Operations
- PySide6.QtGui.QTransform.m13()¶
- Return type
float
Returns the horizontal projection factor.
See also
translate()
Basic Matrix Operations
- PySide6.QtGui.QTransform.m21()¶
- Return type
float
Returns the horizontal shearing factor.
See also
shear()
Basic Matrix Operations
- PySide6.QtGui.QTransform.m22()¶
- Return type
float
Returns the vertical scaling factor.
See also
scale()
Basic Matrix Operations
- PySide6.QtGui.QTransform.m23()¶
- Return type
float
Returns the vertical projection factor.
See also
translate()
Basic Matrix Operations
- PySide6.QtGui.QTransform.m31()¶
- Return type
float
Returns the horizontal translation factor.
See also
dx()
translate()
Basic Matrix Operations
- PySide6.QtGui.QTransform.m32()¶
- Return type
float
Returns the vertical translation factor.
See also
dy()
translate()
Basic Matrix Operations
- PySide6.QtGui.QTransform.m33()¶
- Return type
float
Returns the division factor.
See also
translate()
Basic Matrix Operations
- PySide6.QtGui.QTransform.map(x, y)¶
- Parameters
x – float
y – float
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' = m11x + m21y + dx y' = m22y + m12x + dy if not isAffine(): w' = m13x + m23y + m33 x' /= w' y' /= w'
The point (x, y) is the original point, and (x’, y’) is the transformed point.
See also
Basic Matrix Operations
- PySide6.QtGui.QTransform.map(r)
- Parameters
- Return type
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.
- PySide6.QtGui.QTransform.map(a)
- Parameters
- Return type
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.
- PySide6.QtGui.QTransform.map(a)
- Parameters
- Return type
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.
- PySide6.QtGui.QTransform.map(p)
- Parameters
- Return type
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.
- PySide6.QtGui.QTransform.map(p)
- Parameters
- Return type
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.
- PySide6.QtGui.QTransform.map(l)
- Parameters
- Return type
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.
- PySide6.QtGui.QTransform.map(p)
- Parameters
- Return type
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.
- PySide6.QtGui.QTransform.map(l)
- Parameters
- Return type
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.
- PySide6.QtGui.QTransform.mapRect(arg__1)¶
- Parameters
arg__1 –
PySide6.QtCore.QRect
- Return type
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.
- PySide6.QtGui.QTransform.mapRect(arg__1)
- Parameters
arg__1 –
PySide6.QtCore.QRectF
- Return type
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' = m11x + m21y + dx y' = m22y + m12x + dy if not isAffine(): w' = m13x + m23y + 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.
See also
mapToPolygon()
Basic Matrix Operations
- PySide6.QtGui.QTransform.mapToPolygon(r)¶
- Parameters
- Return type
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' = m11x + m21y + dx y' = m22y + m12x + dy if not isAffine(): w' = m13x + m23y + 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)
.
See also
mapRect()
Basic Matrix Operations
- PySide6.QtGui.QTransform.__ne__(arg__1)¶
- Parameters
arg__1 –
PySide6.QtGui.QTransform
- Return type
bool
Returns true
if this matrix is not equal to the given matrix
, otherwise returns false
.
- PySide6.QtGui.QTransform.__mul__(n)¶
- Parameters
n – float
- Return type
- PySide6.QtGui.QTransform.__mul__(o)
- Parameters
- Return type
Returns the result of multiplying this matrix by the given matrix
.
Note that matrix multiplication is not commutative, i.e. a*b != b*a.
- PySide6.QtGui.QTransform.__imul__(arg__1)¶
- Parameters
arg__1 –
PySide6.QtGui.QTransform
- Return type
This is an overloaded function.
Returns the result of multiplying this matrix by the given matrix
.
- PySide6.QtGui.QTransform.__imul__(div)
- Parameters
div – float
- Return type
This is an overloaded function.
Returns the result of performing an element-wise multiplication of this matrix with the given scalar
.
- PySide6.QtGui.QTransform.__add__(n)¶
- Parameters
n – float
- Return type
- PySide6.QtGui.QTransform.__iadd__(div)¶
- Parameters
div – float
- Return type
This is an overloaded function.
Returns the matrix obtained by adding the given scalar
to each element of this matrix.
- PySide6.QtGui.QTransform.__sub__(n)¶
- Parameters
n – float
- Return type
- PySide6.QtGui.QTransform.__isub__(div)¶
- Parameters
div – float
- Return type
This is an overloaded function.
Returns the matrix obtained by subtracting the given scalar
from each element of this matrix.
- PySide6.QtGui.QTransform.__div__(n)¶
- Parameters
n – float
- Return type
- PySide6.QtGui.QTransform.__idiv__(div)¶
- Parameters
div – float
- Return type
This is an overloaded function.
Returns the result of performing an element-wise division of this matrix by the given scalar
.
- PySide6.QtGui.QTransform.__eq__(arg__1)¶
- Parameters
arg__1 –
PySide6.QtGui.QTransform
- Return type
bool
Returns true
if this matrix is equal to the given matrix
, otherwise returns false
.
- static PySide6.QtGui.QTransform.quadToQuad(arg__1, arg__2)¶
- Parameters
arg__1 –
PySide6.QtGui.QPolygonF
arg__2 –
PySide6.QtGui.QPolygonF
- Return type
object
- static PySide6.QtGui.QTransform.quadToQuad(one, two, result)
- Parameters
one –
PySide6.QtGui.QPolygonF
two –
PySide6.QtGui.QPolygonF
result –
PySide6.QtGui.QTransform
- Return type
bool
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.
See also
- static PySide6.QtGui.QTransform.quadToSquare(arg__1)¶
- Parameters
arg__1 –
PySide6.QtGui.QPolygonF
- Return type
object
- static PySide6.QtGui.QTransform.quadToSquare(quad, result)
- Parameters
quad –
PySide6.QtGui.QPolygonF
result –
PySide6.QtGui.QTransform
- Return type
bool
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.
See also
- PySide6.QtGui.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.
See also
QTransform()
isIdentity()
Basic Matrix Operations
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.
See also
- PySide6.QtGui.QTransform.rotateRadians(a[, axis=Qt.ZAxis])¶
- Parameters
a – float
axis –
Axis
- Return type
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.
See also
- PySide6.QtGui.QTransform.scale(sx, sy)¶
- Parameters
sx – float
sy – float
- Return type
Scales the coordinate system by sx
horizontally and sy
vertically, and returns a reference to the matrix.
See also
- PySide6.QtGui.QTransform.setMatrix(m11, m12, m13, m21, m22, m23, m31, m32, m33)¶
- Parameters
m11 – float
m12 – float
m13 – float
m21 – float
m22 – float
m23 – float
m31 – float
m32 – float
m33 – float
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.
See also
QTransform()
- PySide6.QtGui.QTransform.shear(sh, sv)¶
- Parameters
sh – float
sv – float
- Return type
Shears the coordinate system by sh
horizontally and sv
vertically, and returns a reference to the matrix.
See also
- static PySide6.QtGui.QTransform.squareToQuad(arg__1)¶
- Parameters
arg__1 –
PySide6.QtGui.QPolygonF
- Return type
object
- static PySide6.QtGui.QTransform.squareToQuad(square, result)
- Parameters
square –
PySide6.QtGui.QPolygonF
result –
PySide6.QtGui.QTransform
- Return type
bool
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.
See also
- PySide6.QtGui.QTransform.translate(dx, dy)¶
- Parameters
dx – float
dy – float
- Return type
Moves the coordinate system dx
along the x axis and dy
along the y axis, and returns a reference to the matrix.
See also
- PySide6.QtGui.QTransform.transposed()¶
- Return type
Returns the transpose of this matrix.
- PySide6.QtGui.QTransform.type()¶
- Return type
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.
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